Journal articles: 'Fatou'

1

Locoh, Thérèse, and Isabelle Puech. "Fatou Sow." Travail, genre et sociétés 43, no. 3 (2019): 4. http://dx.doi.org/10.3917/tgs.000.0004.

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WOLD, ERLEND FORNÆSS. "FATOU–BIEBERBACH DOMAINS." International Journal of Mathematics 16, no. 10 (November 2005): 1119–30. http://dx.doi.org/10.1142/s0129167x05003235.

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We show that for any m ∈ ℕ ∪ {∞}, there exist m disjoint FB (Fatou–Bieberbach) domains whose union is dense in ℂk. In fact, we show that any point not in the union is a boundary point for all the domains. We construct FB domains that contains arbitrary countable collections of subvarieties of ℂk, and we construct FB domains that intersect elements of countable collections of affine subspaces of ℂk in connected proper subsets. Moreover, we show that any Runge FB domain is the attracting basin for a sequence of automorphisms of ℂk, although not necessarily if you only allow iteration of one automorphism. We also show that an increasing sequence of Runge ℂk's is a ℂk.

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3

Tarot, Laure, Fatou Kandé Senghor, and Christine Eyene. "Fatou Kandé Senghor." Africultures 85, no. 3 (2011): 88. http://dx.doi.org/10.3917/afcul.085.0088.

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4

Robertson, John W. "Fatou maps inℙndynamics." International Journal of Mathematics and Mathematical Sciences 2003, no. 19 (2003): 1233–40. http://dx.doi.org/10.1155/s0161171203208048.

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We study the dynamics of a holomorphic self-mapfof complex projective space of degreed>1by utilizing the notion of a Fatou map, introduced originally by Ueda (1997) and independently by the author (2000). A Fatou map is intuitively like an analytic subvariety on which the dynamics offare a normal family (such as a local stable manifold of a hyperbolic periodic point). We show that global stable manifolds of hyperbolic fixed points are given by Fatou maps. We further show that they are necessarily Kobayashi hyperbolic and are always ramified byf(and therefore any hyperbolic periodic point attracts a point of the critical set off). We also show that Fatou components are hyperbolically embedded inℙnand that a Fatou component which is attracted to a taut subset of itself is necessarily taut.

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5

Vitali, Ilaria. "Fatou Diome, Sognando Maldini." Studi Francesi, no. 148 (XLX | I) (April 1, 2006): 201. http://dx.doi.org/10.4000/studifrancesi.30901.

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6

Mair, B. A., and David Singman. "A generalized Fatou theorem." Transactions of the American Mathematical Society 300, no. 2 (February 1, 1987): 705. http://dx.doi.org/10.1090/s0002-9947-1987-0876474-7.

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Mair, B. A., Stanton Philipp, and David Singman. "A converse Fatou theorem." Michigan Mathematical Journal 36, no. 1 (1989): 3–9. http://dx.doi.org/10.1307/mmj/1029003878.

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8

Jurney, Florence Ramond, and Fatou Diome. "Entretien avec Fatou Diome." Women in French Studies 18, no. 1 (2010): 148–59. http://dx.doi.org/10.1353/wfs.2010.0022.

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9

Bensouda, Fatou. "Remarks by Fatou Bensouda." Proceedings of the ASIL Annual Meeting 107 (2013): 407–20. http://dx.doi.org/10.1017/s0272503700072244.

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10

Asuke, Taro. "On Fatou-Julia decompositions." Annales de la faculté des sciences de Toulouse Mathématiques 22, no. 1 (2013): 155–95. http://dx.doi.org/10.5802/afst.1369.

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11

Globevnik, Josip. "On Fatou-Bieberbach domains." Mathematische Zeitschrift 229, no. 1 (September 1998): 91–106. http://dx.doi.org/10.1007/pl00004653.

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12

Loeb, Peter A., and Yeneng Sun. "A general Fatou Lemma." Advances in Mathematics 213, no. 2 (August 2007): 741–62. http://dx.doi.org/10.1016/j.aim.2007.01.008.

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13

Khan, M. Ali, Nobusumi Sagara, and Takashi Suzuki. "An exact Fatou lemma for Gelfand integrals: a characterization of the Fatou property." Positivity 20, no. 2 (August 21, 2015): 343–54. http://dx.doi.org/10.1007/s11117-015-0359-z.

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14

BOC-THALER, LUKA, JOHN ERIK FORNÆSS, and HAN PETERS. "Fatou components with punctured limit sets." Ergodic Theory and Dynamical Systems 35, no. 5 (April 23, 2014): 1380–93. http://dx.doi.org/10.1017/etds.2013.115.

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We study invariant Fatou components for holomorphic endomorphisms in $\mathbb{P}^{2}$. In the recurrent case these components were classified by Fornæss and Sibony [Classification of recurrent domains for some holomorphic maps. Math. Ann. 301(4) (1995), 813–820]. Ueda [Holomorphic maps on projective spaces and continuations of Fatou maps. Michigan Math J.56(1) (2008), 145–153] completed this classification by proving that it is not possible for the limit set to be a punctured disk. Recently Lyubich and Peters [Classification of invariant Fatou components for dissipative Hénon maps. Preprint] classified non-recurrent invariant Fatou components, under the additional hypothesis that the limit set is unique. Again all possibilities in this classification were known to occur, except for the punctured disk. Here we show that the punctured disk can indeed occur as the limit set of a non-recurrent Fatou component. We provide many additional examples of holomorphic and polynomial endomorphisms of $\mathbb{C}^{2}$ with non-recurrent Fatou components on which the orbits converge to the regular part of arbitrary analytic sets.

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15

Jha, Nabonarayan, and Jaynarayan Jha. "On Fatou Topologies of Inextensible Riesz Spaces." Tribhuvan University Journal 35, no. 2 (December 31, 2020): 12–21. http://dx.doi.org/10.3126/tuj.v35i2.36184.

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In this paper we shall discuss the general properties of Fatou topologies on Inextensible Riesz Spaces. We find that on a given inextensible Riesz Spaces, there may be no non-trival Fatou topologies but if it has any Hausdorff Fatou topology, it has only one and this has several special properties.

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16

Lesne, Élisabeth. "Fatou Diome, Celles qui attendent." Hommes & migrations, no. 1286-1287 (July 1, 2010): 316–137. http://dx.doi.org/10.4000/hommesmigrations.1693.

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17

Kamaly, A., and A. M. Stokolos. "On the quantitative Fatou property." Colloquium Mathematicum 91, no. 2 (2002): 303–11. http://dx.doi.org/10.4064/cm91-2-9.

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18

Charak, K. S., A. Singh, and M. Kumar. "Fatou and Julia like sets." Ukrains’kyi Matematychnyi Zhurnal 73, no. 10 (October 17, 2021): 1432–38. http://dx.doi.org/10.37863/umzh.v73i10.802.

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19

Haskell, Rosemary. "Fatou DiomeLes veilleurs de Sangomar." World Literature Today 94, no. 4 (2020): 100–101. http://dx.doi.org/10.1353/wlt.2020.0097.

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20

Biondi, Carminella. "Fatou Diome, Inassouvies nos vies." Studi Francesi, no. 163 (LV | I) (May 1, 2011): 224–25. http://dx.doi.org/10.4000/studifrancesi.6130.

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21

Pessini, Elena. "Fatou Diome, Inassouvies nos vies." Studi Francesi, no. 158 (LIII | II) (July 1, 2009): 450. http://dx.doi.org/10.4000/studifrancesi.8105.

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22

Rippon, P. J., and G. M. Stallard. "Boundaries of escaping Fatou components." Proceedings of the American Mathematical Society 139, no. 08 (August 1, 2011): 2807. http://dx.doi.org/10.1090/s0002-9939-2011-10842-6.

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23

Ma��, Ricardo. "On a theorem of Fatou." Boletim da Sociedade Brasileira de Matem�tica 24, no. 1 (March 1993): 1–11. http://dx.doi.org/10.1007/bf01231694.

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24

Sweezy, Caroline. "Fatou theorems for parabolic equations." Proceedings of the American Mathematical Society 124, no. 8 (August 1, 1996): 2343–55. http://dx.doi.org/10.1090/s0002-9939-96-03687-8.

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25

KHOAI, HA HUY. "p-ADIC FATOU–BIEBERBACH MAPPINGS." International Journal of Mathematics 16, no. 03 (March 2005): 303–6. http://dx.doi.org/10.1142/s0129167x05002862.

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26

Gorbovickis, Igors. "On multi-dimensional Fatou bifurcation." Bulletin des Sciences Mathématiques 138, no. 3 (April 2014): 356–75. http://dx.doi.org/10.1016/j.bulsci.2013.06.002.

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27

Buff, Xavier. "Wandering Fatou component for polynomials." Annales de la faculté des sciences de Toulouse Mathématiques 27, no. 2 (2018): 445–75. http://dx.doi.org/10.5802/afst.1575.

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28

Biondi, Carminella. "Fatou Diome, Impossible de grandir." Studi Francesi, no. 172 (LVIII | I) (April 1, 2014): 194–95. http://dx.doi.org/10.4000/studifrancesi.2311.

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29

Cao, Chun-Lei, and Yue-Fei Wang. "On completely invariant Fatou components." Arkiv för Matematik 41, no. 2 (October 2003): 253–65. http://dx.doi.org/10.1007/bf02390814.

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30

Maggis, Marco, Thilo Meyer-Brandis, and Gregor Svindland. "Fatou closedness under model uncertainty." Positivity 22, no. 5 (March 24, 2018): 1325–43. http://dx.doi.org/10.1007/s11117-018-0578-1.

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31

Chen, Shengzhong, Niushan Gao, and Foivos Xanthos. "The strong Fatou property of risk measures." Dependence Modeling 6, no. 1 (October 1, 2018): 183–96. http://dx.doi.org/10.1515/demo-2018-0012.

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AbstractIn this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property,whichwas introduced in [19], seems to be most suitable to ensure nice dual representations of risk measures. Our main result asserts that every quasiconvex law-invariant functional on a rearrangement invariant space X with the strong Fatou property is (X, L1) lower semicontinuous and that the converse is true on a wide range of rearrangement invariant spaces. We also study inf-convolutions of law-invariant or surplus-invariant risk measures that preserve the (strong) Fatou property.

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32

PETERS, HAN, and JASMIN RAISSY. "Fatou components of elliptic polynomial skew products." Ergodic Theory and Dynamical Systems 39, no. 8 (November 28, 2017): 2235–47. http://dx.doi.org/10.1017/etds.2017.112.

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We investigate the description of Fatou components for polynomial skew products in two complex variables. The non-existence of wandering domains near a super-attracting invariant fiber was shown in Lilov [Fatou theory in two dimensions. PhD Thesis, University of Michigan, 2004], and the geometrically attracting case was studied in Peters and Vivas [Polynomial skew products with wandering Fatou-disks. Math. Z.283(1–2) (2016), 349–366] and Peters and Smit [Fatou components of attracting skew products. Preprint, 2015, http://arxiv.org/abs/1508.06605]. In Astorg et al [A two-dimensional polynomial mapping with a wandering Fatou component. Ann. of Math. (2), 184 (2016), 263–313] it was proven that wandering domains can exist near a parabolic invariant fiber. In this paper we study the remaining case, namely the dynamics near an elliptic invariant fiber. We prove that the two-dimensional Fatou components near the elliptic invariant fiber correspond exactly to the Fatou components of the restriction to the fiber, under the assumption that the multiplier at the elliptic invariant fiber satisfies the Brjuno condition and that the restriction polynomial has no critical points on the Julia set. We also show the description does not hold when the Brjuno condition is dropped. Our main tool is the construction of expanding metrics on nearby fibers, and one of the key steps in this construction is given by a local description of the dynamics near a parabolic periodic cycle.

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33

NICKS, DANIEL A., and DAVID J. SIXSMITH. "Hollow quasi-Fatou components of quasiregular maps." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 3 (September 23, 2016): 561–74. http://dx.doi.org/10.1017/s0305004116000840.

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AbstractWe define a quasi-Fatou component of a quasiregular map as a connected component of the complement of the Julia set. A domain in ℝd is called hollow if it has a bounded complementary component. We show that for each d ⩾ 2 there exists a quasiregular map of transcendental type f: ℝd → ℝd with a quasi-Fatou component which is hollow.Suppose that U is a hollow quasi-Fatou component of a quasiregular map of transcendental type. We show that if U is bounded, then U has many properties in common with a multiply connected Fatou component of a transcendental entire function. On the other hand, we show that if U is not bounded, then it is completely invariant and has no unbounded boundary components. We show that this situation occurs if J(f) has an isolated point, or if J(f) is not equal to the boundary of the fast escaping set. Finally, we deduce that if J(f) has a bounded component, then all components of J(f) are bounded.

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34

Dehon, Claire L. "Celles qui attendent by Fatou Diome." French Review 85, no. 3 (2012): 587–88. http://dx.doi.org/10.1353/tfr.2012.0396.

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35

Charak, Kuldeep, Anil Singh, and Manish Kumar. "Fatou and Julia like sets II." Filomat 35, no. 8 (2021): 2721–30. http://dx.doi.org/10.2298/fil2108721c.

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This paper is a continuation of authors work: Fatou and Julia like sets, Ukranian Math. J., to appear/arXiv:2006.08308[math.CV](see [5]). Here, we introduce escaping like set and generalized escaping like set for a family of holomorphic functions on an arbitrary domain, and establish some distinctive properties of these sets. The connectedness of the Julia like set is also proved.

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36

Ousselin, Edward. "Inassouvies, nos vies by Fatou Diome." World Literature Today 83, no. 2 (2009): 65. http://dx.doi.org/10.1353/wlt.2009.0255.

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37

Singh, Anand Prakash. "Unbounded components of the fatou set." Complex Variables, Theory and Application: An International Journal 41, no. 2 (April 2000): 133–44. http://dx.doi.org/10.1080/17476930008815242.

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38

Sixsmith, D. J. "Simply Connected Fast Escaping Fatou Components." Pure and Applied Mathematics Quarterly 8, no. 4 (2012): 1029–46. http://dx.doi.org/10.4310/pamq.2012.v8.n4.a10.

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39

Rochon, Dominic. "On a Generalized Fatou-Julia Theorem." Fractals 11, no. 03 (September 2003): 213–19. http://dx.doi.org/10.1142/s0218348x03002075.

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In this article, we continue to explore some specific results in bicomplex dynamics. In particular, we give a bicomplex version of the so-called Fatou-Julia theorem. In fact, we give a complete topological characterization in ℝ4 of the bicomplex filled-Julia set for a quadratic polynomial in bicomplex numbers of the form w2 + c.

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40

Rippon, P. J., and G. M. Stallard. "On questions of Fatou and Eremenko." Proceedings of the American Mathematical Society 133, no. 4 (October 18, 2004): 1119–26. http://dx.doi.org/10.1090/s0002-9939-04-07805-0.

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41

Bolsch, A. "Periodic Fatou Components of Meromorphic Functions." Bulletin of the London Mathematical Society 31, no. 5 (September 1999): 543–55. http://dx.doi.org/10.1112/s0024609399005950.

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42

Poon, Kin-Keung. "Fatou-Julia theory on transcendental semigroups." Bulletin of the Australian Mathematical Society 58, no. 3 (December 1998): 403–10. http://dx.doi.org/10.1017/s000497270003238x.

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In this paper, we shall study the dynamics on transcendental semigroups. Several properties of Fatou and Julia sets of transcendental semigroups will be explored. Moreover, we shall investigate some properties of Abelian transcendental semigroups and wandering domains of transcendental semigroups.

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43

Zieba, Wies?aw. "A note on conditional Fatou Lemma." Probability Theory and Related Fields 78, no. 1 (1988): 73–74. http://dx.doi.org/10.1007/bf00718036.

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44

Peters, Han, and Iris Marjan Smit. "Fatou Components of Attracting Skew-Products." Journal of Geometric Analysis 28, no. 1 (April 6, 2017): 84–110. http://dx.doi.org/10.1007/s12220-017-9811-6.

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45

Cui, GuiZhen, and WenJuan Peng. "On the structure of Fatou domains." Science in China Series A: Mathematics 51, no. 7 (June 21, 2008): 1167–86. http://dx.doi.org/10.1007/s11425-008-0056-5.

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46

Barański, Krzysztof, Núria Fagella, Xavier Jarque, and Bogusława Karpińska. "Accesses to infinity from Fatou components." Transactions of the American Mathematical Society 369, no. 3 (May 2, 2016): 1835–67. http://dx.doi.org/10.1090/tran/6739.

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47

Weickert, Brendan J. "Nonwandering, nonrecurrent Fatou components in P2." Pacific Journal of Mathematics 211, no. 2 (October 1, 2003): 391–97. http://dx.doi.org/10.2140/pjm.2003.211.391.

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48

Peters, Han, and Crystal Zeager. "Tautness and Fatou Components in ℙ2." Journal of Geometric Analysis 22, no. 4 (April 27, 2011): 934–41. http://dx.doi.org/10.1007/s12220-011-9221-0.

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49

Bortz, Simon, and Steve Hofmann. "Quantitative Fatou Theorems and Uniform Rectifiability." Potential Analysis 53, no. 1 (February 12, 2019): 329–55. http://dx.doi.org/10.1007/s11118-019-09771-1.

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50

Pilgrim, Kevin M. "Rational maps whose Fatou components are Jordan domains." Ergodic Theory and Dynamical Systems 16, no. 6 (December 1996): 1323–43. http://dx.doi.org/10.1017/s0143385700010051.

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AbstractWe prove: If f(z) is a critically finite rational map which has exactly two critical points and which is not conjugate to a polynomial, then the boundary of every Fatou component of f is a Jordan curve. If f(z) is a hyperbolic critically finite rational map all of whose postcritical points are periodic, then there exists a cycle of Fatou components whose boundaries are Jordan curves. We give examples of critically finite hyperbolic rational maps f with a Fatou component ω satisfying f(ω) = ω and f|∂ω not topologically conjugate to the dynamics of any polynomial on its Julia set.

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Journal articles on the topic 'Fatou'

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