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This article is cited in 12 scientific papers (total in 12 papers)
Detection of Phase Space Structures of the Cat Map with Lagrangian Descriptors
Víctor J. García-Garridoab, Francisco Balibrea-Iniestaa, Stephen Wigginsc, Ana M. Manchoa, Carlos Lopesinoa a Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM,
C/Nicolás Cabrera 15, Campus Cantoblanco UAM, 28049, Madrid, Spain
b Departamento de Física y Matemáticas,
Universidad de Alcalá, 28871, Alcalá de Henares, Spain
c School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
Abstract:
The goal of this paper is to apply Lagrangian Descriptors (LDs), a technique based on Dynamical Systems Theory (DST) to reveal the phase space structures present in the wellknown Arnold’s cat map. This discrete dynamical system, which represents a classical example of an Anosov diffeomorphism that is strongly mixing, will provide us with a benchmark model to test the performance of LDs and their capability to detect fixed points, periodic orbits and their stable and unstable manifolds present in chaotic maps. In this work we show, both from a theoretical and a numerical perspective, how LDs reveal the invariant manifolds of the periodic orbits of the cat map. The application of this methodology in this setting clearly illustrates the chaotic behavior of the cat map and highlights some technical numerical difficulties that arise in the identification of its phase space structures.
Keywords:
dynamical systems, maps, Lagrangian descriptors, chaotic sets, stable and unstable manifolds, mixing.
Received: 26.07.2018 Accepted: 11.10.2018
Citation:
Víctor J. García-Garrido, Francisco Balibrea-Iniesta, Stephen Wiggins, Ana M. Mancho, Carlos Lopesino, “Detection of Phase Space Structures of the Cat Map with Lagrangian Descriptors”, Regul. Chaotic Dyn., 23:6 (2018), 751–766
Linking options:
https://www.mathnet.ru/eng/rcd364 https://www.mathnet.ru/eng/rcd/v23/i6/p751
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Abstract page: | 160 | References: | 32 |
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