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Journal articles on the topic 'Operador de Ruelle'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

YE, YUAN-LING. "Ruelle operator with weakly contractive iterated function systems." Ergodic Theory and Dynamical Systems 33, no. 4 (2012): 1265–90. http://dx.doi.org/10.1017/s0143385712000211.

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AbstractThe Ruelle operator has been studied extensively both in dynamical systems and iterated function systems (IFSs). Given a weakly contractive IFS $(X, \{w_j\}_{j=1}^m)$ and an associated family of positive continuous potential functions $\{p_j\}_{j=1}^m$, a triple system $(X, \{w_j\}_{j=1}^m, \{p_j\}_{j=1}^m)$is set up. In this paper we study Ruelle operators associated with the triple systems. The paper presents an easily verified condition. Under this condition, the Ruelle operator theorem holds provided that the potential functions are Dini continuous. Under the same condition, the Ru

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2

JIANG, YUNPING, and YUAN-LING YE. "Ruelle operator theorem for non-expansive systems." Ergodic Theory and Dynamical Systems 30, no. 2 (2009): 469–87. http://dx.doi.org/10.1017/s014338570900025x.

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AbstractThe Ruelle operator theorem has been studied extensively both in dynamical systems and iterated function systems. In this paper we study the Ruelle operator theorem for non-expansive systems. Our theorems give some sufficient conditions for the Ruelle operator theorem to be held for a non-expansive system.

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3

Bessa, Mário, and Manuel Stadlbauer. "On the Lyapunov spectrum of relative transfer operators." Stochastics and Dynamics 16, no. 06 (2016): 1650024. http://dx.doi.org/10.1142/s0219493716500246.

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We analyze the Lyapunov spectrum of the relative Ruelle operator associated with a skew product whose base is an ergodic automorphism and whose fibers are full shifts. We prove that these operators can be approximated in the [Formula: see text]-topology by positive matrices with an associated dominated splitting.

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4

Cioletti, L., and A. O. Lopes. "Correlation inequalities and monotonicity properties of the Ruelle operator." Stochastics and Dynamics 19, no. 06 (2019): 1950048. http://dx.doi.org/10.1142/s0219493719500485.

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In this paper, we provide sufficient conditions for the validity of the FKG Inequality, on Thermodynamic Formalism setting, for a class of eigenmeasures of the dual of the Ruelle operator. We use this correlation inequality to study the maximal eigenvalue problem for the Ruelle operator associated to low regular potentials. As an application, we obtain explicit upper bounds for the main eigenvalue (consequently, for the pressure) of the Ruelle operator associated to Ising models with a power law decay interaction energy.

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5

Giulietti, P., A. O. Lopes, and V. Pit. "Duality between eigenfunctions and eigendistributions of Ruelle and Koopman operators via an integral kernel." Stochastics and Dynamics 16, no. 03 (2016): 1660011. http://dx.doi.org/10.1142/s021949371660011x.

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We consider the classical dynamics given by a one-sided shift on the Bernoulli space of [Formula: see text] symbols. We study, on the space of Hölder functions, the eigendistributions of the Ruelle operator with a given potential. Our main theorem shows that for any isolated eigenvalue, the eigendistributions of such Ruelle operator are dual to eigenvectors of a Ruelle operator with a conjugate potential. We also show that the eigenfunctions and eigendistributions of the Koopman operator satisfy a similar relationship. To show such results we employ an integral kernel technique, where the kern

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6

Fan, Aihua, and Yunping Jiang. "On Ruelle-Perron-Frobenius Operators.¶I. Ruelle Theorem." Communications in Mathematical Physics 223, no. 1 (2001): 125–41. http://dx.doi.org/10.1007/s002200100538.

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7

Tasaki, S. "On Prigogine's approaches to irreversibility: a case study by the baker map." Discrete Dynamics in Nature and Society 2004, no. 1 (2004): 251–72. http://dx.doi.org/10.1155/s1026022604312069.

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The baker map is investigated by two different theories of irreversibility by Prigogine and his colleagues, namely, theΛ-transformation and complex spectral theories, and their structures are compared. In both theories, the evolution operatorU†of observables (the Koopman operator) is found to acquire dissipativityby restrictingobservables to an appropriate subspaceΦof the Hilbert spaceL2of square integrable functions. Consequently, its spectral set contains an annulus in the unit disc. However, the two theories are not equivalent. In theΛ-transformation theory, a bijective mapΛ†−1:Φ→L2is looke

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8

Stoyanov, Luchezar. "On Gibbs Measures and Spectra of Ruelle Transfer Operators." Canadian Mathematical Bulletin 60, no. 2 (2017): 411–21. http://dx.doi.org/10.4153/cmb-2016-073-2.

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AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

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9

Lau, Ka-Sing, and Yuan-Ling Ye. "Ruelle operator with nonexpansive IFS." Studia Mathematica 148, no. 2 (2001): 143–69. http://dx.doi.org/10.4064/sm148-2-4.

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10

Ye, Yuan-Ling. "Vector-valued Ruelle operators." Journal of Mathematical Analysis and Applications 299, no. 2 (2004): 341–56. http://dx.doi.org/10.1016/j.jmaa.2004.02.058.

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11

Jorgensen, Palle E. T. "Ruelle operators: functions which are harmonic with respect to a transfer operator." Memoirs of the American Mathematical Society 152, no. 720 (2001): 0. http://dx.doi.org/10.1090/memo/0720.

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12

Domínguez, Patricia, Peter Makienko, and Guillermo Sienra. "Ruelle operator and transcendental entire maps." Discrete & Continuous Dynamical Systems - A 12, no. 4 (2005): 773–89. http://dx.doi.org/10.3934/dcds.2005.12.773.

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13

Fan, Ai Hua, and Ka-Sing Lau. "Iterated Function System and Ruelle Operator." Journal of Mathematical Analysis and Applications 231, no. 2 (1999): 319–44. http://dx.doi.org/10.1006/jmaa.1998.6210.

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14

MATSUI, TAKU. "ON NON-COMMUTATIVE RUELLE TRANSFER OPERATOR." Reviews in Mathematical Physics 13, no. 10 (2001): 1183–201. http://dx.doi.org/10.1142/s0129055x01001034.

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15

FAN, AI HUA. "A PROOF OF THE RUELLE OPERATOR THEOREM." Reviews in Mathematical Physics 07, no. 08 (1995): 1241–47. http://dx.doi.org/10.1142/s0129055x95000451.

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16

Lopes, Artur O., and Victor Vargas. "The Ruelle operator for symmetric $\beta$-shifts." Publicacions Matemàtiques 64 (July 1, 2020): 661–80. http://dx.doi.org/10.5565/publmat6422012.

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17

TSUJII, MASATO. "A simple proof for monotonicity of entropy in the quadratic family." Ergodic Theory and Dynamical Systems 20, no. 3 (2000): 925–33. http://dx.doi.org/10.1017/s014338570000050x.

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18

STOYANOV, LUCHEZAR. "Non-integrability of open billiard flows and Dolgopyat-type estimates." Ergodic Theory and Dynamical Systems 32, no. 1 (2011): 295–313. http://dx.doi.org/10.1017/s0143385710000933.

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AbstractWe consider open billiard flows in ℝn and show that the standard symplectic form dα in ℝn satisfies a specific non-integrability condition over their non-wandering sets Λ. This allows one to use the main result in Stoyanov [Spectra of Ruelle transfer operators for Axiom A flows. Preprint, 2010, arXiv:0810.1126v4 [math.DS]] and obtain Dolgopyat-type estimates for the spectra of Ruelle transfer operators under simpler conditions. We also describe a class of open billiard flows in ℝn(n≥3) satisfying a certain pinching condition, which in turn implies that the (un)stable laminations over t

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19

Lopes, A. O., and Ph Thieullen. "Eigenfunctions of the Laplacian and associated Ruelle operator." Nonlinearity 21, no. 10 (2008): 2239–53. http://dx.doi.org/10.1088/0951-7715/21/10/003.

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20

Baraviera, Alexandre, Artur O. Lopes, and Ruy Exel. "A Ruelle Operator for continuous time Markov Chains." São Paulo Journal of Mathematical Sciences 4, no. 1 (2010): 1. http://dx.doi.org/10.11606/issn.2316-9028.v4i1p1-16.

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21

Levin, G. M., M. L. Sodin, and P. M. Yuditski. "A Ruelle operator for a real Julia set." Communications in Mathematical Physics 141, no. 1 (1991): 119–32. http://dx.doi.org/10.1007/bf02100007.

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22

Chen, Xiao-Peng, Li-Yan Wu, and Yuan-Ling Ye. "Ruelle operator for infinite conformal iterated function systems." Chaos, Solitons & Fractals 45, no. 12 (2012): 1521–30. http://dx.doi.org/10.1016/j.chaos.2012.09.001.

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23

Ye, Yuan-Ling. "Vector-valued Ruelle operator with weakly contractive IFS." Journal of Mathematical Analysis and Applications 330, no. 1 (2007): 221–36. http://dx.doi.org/10.1016/j.jmaa.2006.07.034.

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24

Ye, Yuan-Ling. "Ruelle operator with nonexpansive IFS on the line." Journal of Mathematical Analysis and Applications 330, no. 1 (2007): 406–15. http://dx.doi.org/10.1016/j.jmaa.2006.07.090.

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25

Naud, Frédéric. "The Ruelle spectrum of generic transfer operators." Discrete & Continuous Dynamical Systems - A 32, no. 7 (2012): 2521–31. http://dx.doi.org/10.3934/dcds.2012.32.2521.

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26

Dutkay, Dorin Ervin. "Harmonic analysis of signed Ruelle transfer operators." Journal of Mathematical Analysis and Applications 273, no. 2 (2002): 590–617. http://dx.doi.org/10.1016/s0022-247x(02)00284-6.

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27

Cioletti, Leandro, Artur O. Lopes, and Manuel Stadlbauer. "Ruelle operator for continuous potentials and DLR-Gibbs measures." Discrete & Continuous Dynamical Systems - A 40, no. 8 (2020): 4625–52. http://dx.doi.org/10.3934/dcds.2020195.

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28

Rugh, Hans Henrik. "The Milnor–Thurston Determinant and the Ruelle Transfer Operator." Communications in Mathematical Physics 342, no. 2 (2015): 603–14. http://dx.doi.org/10.1007/s00220-015-2515-5.

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29

Petkov, Vesselin, and Luchezar Stoyanov. "Ruelle operators with two complex parameters and applications." Comptes Rendus Mathematique 353, no. 7 (2015): 595–99. http://dx.doi.org/10.1016/j.crma.2015.04.005.

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30

Fan, Aihua, and Yunping Jiang. "On Ruelle-Perron-Frobenius Operators.¶II. Convergence Speeds." Communications in Mathematical Physics 223, no. 1 (2001): 143–59. http://dx.doi.org/10.1007/s002200100539.

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31

Levin, G., M. Sodin, and P. Yuditskii. "Ruelle operators with rational weights for Julia sets." Journal d'Analyse Mathématique 63, no. 1 (1994): 303–31. http://dx.doi.org/10.1007/bf03008428.

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32

WALTERS, PETER. "A natural space of functions for the Ruelle operator theorem." Ergodic Theory and Dynamical Systems 27, no. 04 (2007): 1323. http://dx.doi.org/10.1017/s0143385707000028.

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33

Straub, Sina. "The Ruelle Transfer Operator in the Context of Orthogonal Polynomials." Complex Analysis and Operator Theory 8, no. 3 (2013): 709–32. http://dx.doi.org/10.1007/s11785-013-0308-4.

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34

OLIVEIRA, KRERLEY, and MARCELO VIANA. "Thermodynamical formalism for robust classes of potentials and non-uniformly hyperbolic maps." Ergodic Theory and Dynamical Systems 28, no. 2 (2008): 501–33. http://dx.doi.org/10.1017/s0143385707001009.

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AbstractWe develop a Ruelle–Perron–Fröbenius transfer operator approach to the ergodic theory of a large class of non-uniformly expanding transformations on compact manifolds. For Hölder continuous potentials not too far from constant, we prove that the transfer operator has a positive eigenfunction, which is piecewise Hölder continuous, and use this fact to show that there is exactly one equilibrium state. Moreover, the equilibrium state is a non-lacunary Gibbs measure, a non-uniform version of the classical notion of Gibbs measure that we introduce here.

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35

Koyama, Shin-ya. "Selberg zeta functions and Ruelle operators for function fields." Proceedings of the Japan Academy, Series A, Mathematical Sciences 67, no. 8 (1991): 255–59. http://dx.doi.org/10.3792/pjaa.67.255.

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36

Tanaka, Haruyoshi. "Spectral properties of a class of generalized Ruelle operators." Hiroshima Mathematical Journal 39, no. 2 (2009): 181–205. http://dx.doi.org/10.32917/hmj/1249046336.

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37

Stoyanov, Luchezar, and Vesselin Petkov. "Ruelle transfer operators with two complex parameters and applications." Discrete and Continuous Dynamical Systems 36, no. 11 (2016): 6413–51. http://dx.doi.org/10.3934/dcds.2016077.

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38

Stoyanov, Luchezar. "Spectra of Ruelle transfer operators for Axiom A flows." Nonlinearity 24, no. 4 (2011): 1089–120. http://dx.doi.org/10.1088/0951-7715/24/4/005.

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39

Dutkay, Dorin Ervin, and Palle E. T. Jorgensen. "Iterated function systems, Ruelle operators, and invariant projective measures." Mathematics of Computation 75, no. 256 (2006): 1931–70. http://dx.doi.org/10.1090/s0025-5718-06-01861-8.

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40

Campbell, J., and Y. Latushkin. "Sharp Estimates in Ruelle Theorems for Matrix Transfer Operators." Communications in Mathematical Physics 185, no. 2 (1997): 379–96. http://dx.doi.org/10.1007/s002200050095.

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41

Alpay, Daniel, Palle Jorgensen, and Izchak Lewkowicz. "Realizations of Infinite Products, Ruelle Operators and Wavelet Filters." Journal of Fourier Analysis and Applications 21, no. 5 (2015): 1034–52. http://dx.doi.org/10.1007/s00041-015-9396-z.

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42

Bogenschütz, Thomas, and Volker Mathias Gundlach. "Ruelle's transfer operator for random subshifts of finite type." Ergodic Theory and Dynamical Systems 15, no. 3 (1995): 413–47. http://dx.doi.org/10.1017/s0143385700008464.

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AbstractWe consider a Ruelle—Perron—Frobenius type of selection procedure for probability measures that are invariant under random subshifts of finite type. In particular we prove that for a class of random functions this method leads to a unique probability exhibiting properties that justify the names Gibbs measure and equilibrium states. In order to do this we introduce the notion of bundle random dynamical systems and provide a theory for their invariant measures as well as give a precise definition of Gibbs measures.

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43

KLOECKNER, BENOÎT R. "An optimal transportation approach to the decay of correlations for non-uniformly expanding maps." Ergodic Theory and Dynamical Systems 40, no. 3 (2018): 714–50. http://dx.doi.org/10.1017/etds.2018.49.

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We consider the transfer operators of non-uniformly expanding maps for potentials of various regularity, and show that a specific property of potentials (‘flatness’) implies a Ruelle–Perron–Frobenius theorem and a decay of the transfer operator of the same speed as that entailed by the constant potential. The method relies neither on Markov partitions nor on inducing, but on functional analysis and duality, through the simplest principles of optimal transportation. As an application, we notably show that for any map of the circle which is expanding outside an arbitrarily flat neutral point, th

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44

Haydn, Nicolai T. A. "Meromorphic extension of the zeta function for Axiom A flows." Ergodic Theory and Dynamical Systems 10, no. 2 (1990): 347–60. http://dx.doi.org/10.1017/s0143385700005587.

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AbstractWe prove the meromorphicity of the zeta function on shifts of finite type for Hölder continuous functions assuming that the essential spectrum of the associated Ruelle operator is contained in the open unit disc. This result allows to extend the region of meromorphicity of the zeta function for Axiom A flows by a strip whose width is determined by the contraction rate of the flow.

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45

Ye, Yuan-Ling. "Convergence speeds of iterations of Ruelle operator with weakly contractive IFS." Journal of Mathematical Analysis and Applications 279, no. 1 (2003): 151–67. http://dx.doi.org/10.1016/s0022-247x(02)00704-7.

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46

Walters, Peter. "Convergence of the Ruelle operator for a function satisfying Bowen’s condition." Transactions of the American Mathematical Society 353, no. 1 (2000): 327–47. http://dx.doi.org/10.1090/s0002-9947-00-02656-8.

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47

Cowen, Robert. "Topological and Measure-Theoretic Conjugacy of Subshifts Using the Ruelle Operator." Journal of the London Mathematical Society s2-41, no. 2 (1990): 261–71. http://dx.doi.org/10.1112/jlms/s2-41.2.261.

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48

Beck, Christian. "From Ruelle's transfer operator to the Schrödinger operator." Physica D: Nonlinear Phenomena 85, no. 4 (1995): 459–67. http://dx.doi.org/10.1016/0167-2789(95)00181-3.

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49

Stoyanov, Luchezar. "Ruelle operators and decay of correlations for contact Anosov flows." Comptes Rendus Mathematique 351, no. 17-18 (2013): 669–72. http://dx.doi.org/10.1016/j.crma.2013.09.012.

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50

Ruelle, David. "Spectral properties of a class of operators associated with maps in one dimension." Ergodic Theory and Dynamical Systems 11, no. 4 (1991): 757–67. http://dx.doi.org/10.1017/s0143385700006465.

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AbstractLet f be a piecewise monotone map of the interval [0,1] to itself, and g a function of bounded variation on [0, 1]. Hofbauer, Keller and Rychlik have studied operators on functions of bounded variation, whereAmong other things, they show that the essential spectral radius of is in many cases strictly smaller than the spectral radius; there exist therefore isolated eigenvalues of finite multiplicity. The purpose of the present paper is to prove similar results for a more general class of operators forming an algebra (and therefore containing sums of operators like ). An analogous extens

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