Relevant bibliographies by topics / Topological horseshoes

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Topological horseshoes'

Author: Grafiati
Published: 9 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Topological horseshoes"

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Kennedy, Judy, and James A. Yorke. "Topological horseshoes." Transactions of the American Mathematical Society 353, no. 6 (2001): 2513–30. http://dx.doi.org/10.1090/s0002-9947-01-02586-7.

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LI, QINGDU, and XIAO-SONG YANG. "A SIMPLE METHOD FOR FINDING TOPOLOGICAL HORSESHOES." International Journal of Bifurcation and Chaos 20, no. 02 (2010): 467–78. http://dx.doi.org/10.1142/s0218127410025545.

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This paper presents an efficient method for finding horseshoes in dynamical systems by using several simple results on topological horseshoes. In this method, a series of points from an attractor of a map (or a Poincaré map) are firstly computed. By dealing with the series, we can not only find the approximate location of each short unstable periodic orbit (UPO), but also learn the dynamics of almost every small neighborhood of the attractor under the map or the reverse map, which is very helpful for finding a horseshoe. The method is illustrated with the Hénon map and two other examples. Sinc
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HUAN, SONGMEI, QINGDU LI, and XIAO-SONG YANG. "HORSESHOES IN A CHAOTIC SYSTEM WITH ONLY ONE STABLE EQUILIBRIUM." International Journal of Bifurcation and Chaos 23, no. 01 (2013): 1350002. http://dx.doi.org/10.1142/s0218127413500028.

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To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.
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YUAN, QUAN, and XIAO-SONG YANG. "COMPUTER ASSISTED VERIFICATION OF CHAOS IN THE SMOOTH CHUA'S EQUATION." International Journal of Bifurcation and Chaos 18, no. 08 (2008): 2391–96. http://dx.doi.org/10.1142/s0218127408021762.

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In this paper, chaos in the smooth Chua's equation is revisited. To confirm the chaotic behavior in the smooth Chua's equation demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a computer assisted verification of existence of horseshoe chaos by virtue of topological horseshoes theory.
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Yang, Xiao-Song. "Topological horseshoes in continuous maps." Chaos, Solitons & Fractals 33, no. 1 (2007): 225–33. http://dx.doi.org/10.1016/j.chaos.2005.12.030.

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LI, QINGDU, and XIAO-SONG YANG. "TWO KINDS OF HORSESHOES IN A HYPERCHAOTIC NEURAL NETWORK." International Journal of Bifurcation and Chaos 22, no. 08 (2012): 1250200. http://dx.doi.org/10.1142/s0218127412502008.

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This paper studies the hyperchaotic dynamics in a four-dimensional Hopfield neural network by virtue of topological horseshoe. Two different horseshoes (chaotic invariant sets) are found in this network with the same parameters. Numerical studies show that the first one expands only one-dimensionally and the second one expands two-dimensionally. Computer simulation also shows that there exists a heteroclinic connection from the second horseshoe to the first one, which indicates that the chaotic set of this system can have a very complicated structure composed of different kinds of expansions.
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YANG, XIAO-SONG. "TOPOLOGICAL HORSESHOES AND COMPUTER ASSISTED VERIFICATION OF CHAOTIC DYNAMICS." International Journal of Bifurcation and Chaos 19, no. 04 (2009): 1127–45. http://dx.doi.org/10.1142/s0218127409023548.

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In this tutorial paper, we present a history of Smale horseshoe and an overview of the progress of topological horseshoe theory. Then we offer a pedagogical exposition of elements of topological horseshoe theory with a lot of examples. Finally we demonstrate some typical applications of topological horseshoe theory to practical dynamical systems.
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GONCHENKO, SERGEY, MING-CHIA LI, and MIKHAIL MALKIN. "GENERALIZED HÉNON MAPS AND SMALE HORSESHOES OF NEW TYPES." International Journal of Bifurcation and Chaos 18, no. 10 (2008): 3029–52. http://dx.doi.org/10.1142/s0218127408022238.

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We study hyperbolic dynamics and bifurcations for generalized Hénon maps in the form [Formula: see text] (with b, α small and γ > 4). Hyperbolic horseshoes with alternating orientation, called half-orientable horseshoes, are proved to represent the nonwandering set of the maps in certain parameter regions. We show that there are infinitely many classes of such horseshoes with respect to the local topological conjugacy. We also study transitions from the usual orientable and nonorientable horseshoes to half-orientable ones (and vice versa) as parameters vary.
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Wójcik, Klaudiusz, and Piotr Zgliczyński. "Topological horseshoes and delay differential equations." Discrete & Continuous Dynamical Systems - A 12, no. 5 (2005): 827–52. http://dx.doi.org/10.3934/dcds.2005.12.827.

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Yuan, Quan, Fang-Yan Yang, and Lei Wang. "A Note on Hidden Transient Chaos in the Lorenz System." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 5 (2017): 427–34. http://dx.doi.org/10.1515/ijnsns-2016-0168.

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AbstractIn this paper, the classic Lorenz system is revisited. Some dynamical behaviors are shown with the Rayleigh number $\rho $ somewhat smaller than the critical value 24.06 by studying the basins characterization of attraction of attractors and tracing the one-dimensional unstable manifold of the origin, indicating some interesting clues for detecting the existence of hidden transient chaos. In addition, horseshoes chaos is verified in the famous system for some parameters corresponding to the hidden transient chaos by the topological horseshoe theory.
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Dissertations / Theses on the topic "Topological horseshoes"

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PIREDDU, MARINA. "Fixed points and chaotic dynamics for expansive-contractive maps in Euclidean spaces, with some applications." Doctoral thesis, Università degli Studi di Udine, 2009. http://hdl.handle.net/10281/46084.

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In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the Paths" method, since we deal with maps that expand the arcs along one direction. Such theory was developed in the planar case by Papini and Zanolin in [11,12] and it has been extended to the N-dimensional framework by the author and Zanolin in [16]. In the bidimensional setting, elementary theorems from plane topology suffice, while in the higher dimension so
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Book chapters on the topic "Topological horseshoes"

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Burra, Lakshmi. "Topological Horseshoes and Coin-Tossing Dynamics." In Chaotic Dynamics in Nonlinear Theory. Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-2092-3_2.

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Díaz, L. J., and K. Gelfert. "Porcupine-Like Horseshoes: Topological and Ergodic Aspects." In Progress and Challenges in Dynamical Systems. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38830-9_12.

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Fan, Qingju. "Topological Horseshoes in a Two-Scrolls Control system." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25002-6_62.

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Gonchenko, S. V., A. S. Gonchenko, and M. I. Malkin. "On Local Topological Classification of Two-Dimensional Orientable, Non-Orientable, and Half-Orientable Horseshoes." In Nonlinear Systems and Complexity. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58062-3_6.

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Gilmore, Robert, and Christophe Letellier. "Peeling Bifurcations." In The Symmetry of Chaos. Oxford University PressNew York, NY, 2007. http://dx.doi.org/10.1093/oso/9780195310658.003.0005.

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Abstract In Chapter 4 we saw that a dynamical system can have many inequivalent double covers, each with the same symmetry group. This was shown explicitly for double covers of adynamical system exhibiting horseshoe dynamics. The four distinct double covers all possessed R z (n) symmetry but possessed different topological indices (no, n1 ) . The rotation axis of the symmetry group R z (n) linked the image dynamical system in four ways (cf. Fig. 4.2). In creating these four distinct double covers we were careful that the rotation axis did not intersect the strange attractor. This is possible a
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Conference papers on the topic "Topological horseshoes"

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Chen, Guangqun, Xiaorong Hu, and Lijuan Chen. "Numerical Research of a Economic Model Based on Topological Horseshoes Theory." In 2013 International Conference on Information Science and Cloud Computing (ISCC). IEEE, 2013. http://dx.doi.org/10.1109/iscc.2013.11.

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Yuan Quan and Yang Xiaosong. "Review of dynamical complexity research based on topological horseshoe theory." In 2008 Chinese Control Conference (CCC). IEEE, 2008. http://dx.doi.org/10.1109/chicc.2008.4605720.

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Wu, Wenjuan, Zengqiang Chen, and Guanrong Chen. "A New Proof for the Existence of Topological Horseshoe in Chen's Attractor." In 2009 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2009. http://dx.doi.org/10.1109/iwcfta.2009.64.

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Wenjuan Wu and Zengqiang Chen. "A new proof for the existence of topological horseshoe in a business cycle model." In 2010 Chinese Control and Decision Conference (CCDC). IEEE, 2010. http://dx.doi.org/10.1109/ccdc.2010.5498517.

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van den Berg, Martijn A., Michael M. J. Proot, and Peter G. Bakker. "A Topological Study of the Genesis of a Horseshoe Vortex in the Symmetry Plane Due to an Adverse Pressure Gradient." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/fed-24926.

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Abstract The present paper describes the genesis of a horseshoe vortex in the symmetry plane in front of a juncture. In contrast to a previous topological investigation, the presence of the obstacle is no longer physically modelled. Instead, the pressure gradient, induced by the obstacle, has been used to represent its influence. Consequently, the results of this investigation can be applied to any symmetrical flow above a flat plate. The genesis of the vortical structure is analysed by using the theory of nonlinear differential equations and the bifurcation theory. In particular, the genesis
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Basu, S., V. Eswaran, and G. Biswas. "Numerical Prediction of Flow and Heat Transfer in a Rectangular Channel With a Built-in Circular Tube." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/htd-24115.

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Abstract Numerical investigation of flow and heat transfer in a rectangular duct with a built-in circular tube has been carried out for a Reynolds number of 1000 and blockage ratio of 0.44. Since the heat transfer in the duct is dictated by the flow structure, the present study is directed toward characterization of the flow structure. To this end, the topological theory shows the promise of becoming a powerful tool for the study of the flow structure. Computations show helical vortex tubes in the wake and existence of horseshoe vortices. The w component of velocity is surprisingly large in fr
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Journal articles
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