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Journal of Difference Equations and Applications Volume 11, 2005 - Issue 12
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Original Articles

Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers

Jeffrey C. Lagarias University of Michigan, Department of Mathematics, Ann Arbor, MI, 48109-1043, USACorrespondence[email protected]
&
Eric Rains University of California-Davis, Department of Mathematics, Davis, CA, 95616-8633, USA
Pages 1089-1108 | Received 25 May 2005, Accepted 05 Jun 2005, Published online: 16 Aug 2006

Citations (16)

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Read on this site (3)

Grant Cairns, Yuri Nikolayevsky & Gavin Rossiter. (2016) Conewise Linear Periodic Maps of the Plane with Integer Coefficients. The American Mathematical Monthly 123:4, pages 363-375.
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Jeffrey C. Lagarias & Eric Rains. (2005) Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra. Journal of Difference Equations and Applications 11:14, pages 1205-1224.
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Jeffrey C. Lagarias & Eric Rains. (2005) Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles. Journal of Difference Equations and Applications 11:13, pages 1137-1163.
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Articles from other publishers (13)

En-Guo Gu, Bo Li, Jun Ni & Zhao Hui He. (2024) Trajectories associated with parabolic and hyperbolic periodic points of piecewise linear area-preserving map. Chaos, Solitons & Fractals 178, pages 114340.
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En-Guo Gu, Zhao Hui He, Jun Ni & Bo Li. (2023) Invariant regions in piecewise linear area-preserving map. Chaos, Solitons & Fractals 169, pages 113308.
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恩国 顾. (2023) Orbital Characteristics Related to Parabolic and Hyperbolic Periodic Points in Lozi Area-Preserving Map. Applied Physics 13:11, pages 453-464.
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Iryna Sushko, Viktor Avrutin & Laura Gardini. (2021) Center Bifurcation in the Lozi Map. International Journal of Bifurcation and Chaos 31:16.
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John A. G. Roberts, Asaki Saito & Franco Vivaldi. (2021) Critical curves of a piecewise linear map. Chaos: An Interdisciplinary Journal of Nonlinear Science 31:7.
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Hassan Najafi Alishah, Pedro Duarte & Telmo Peixe. (2020) Asymptotic Poincaré maps along the edges of polytopes. Nonlinearity 33:1, pages 469-510.
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Luis Benadero Garcia-Morato, Emilio Freire Macias, Enrique Ponce Nuñez & Francisco Torres Peral. (2018) Bifurcation Patterns in Homogeneous Area-Preserving Piecewise-Linear Maps. Qualitative Theory of Dynamical Systems 18:2, pages 547-582.
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En-Guo Gu. (2019) On the Existence of Chaos in a Discontinuous Area-Preserving Map Arising in Financial Markets. International Journal of Bifurcation and Chaos 28:14, pages 1850177.
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D J W Simpson. (2017) The structure of mode-locking regions of piecewise-linear continuous maps: I. Nearby mode-locking regions and shrinking points. Nonlinearity 30:1, pages 382-444.
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D. J. W. Simpson. (2016) Border-Collision Bifurcations in $\mathbb{R}^N$. SIAM Review 58:2, pages 177-226.
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John A.G. Roberts & Franco Vivaldi. (2015) Arithmetic exponents in piecewise-affine planar maps. Physica D: Nonlinear Phenomena 298-299, pages 1-12.
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Zeraoulia Elhadj. 2013. Lozi Mappings. Lozi Mappings 263 303 .
En_-Guo GU, En-Guo GU, Zhao Hui He, Jun Ni & Bo Li. (2022) Invariant Regions in Piecewise Linear Area-Preserving Map. SSRN Electronic Journal.
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