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Homoclinic trajectories and chaotic behaviour in a piecewise linear oscillator
Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphisms
1. | Departamento de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo |
2. | Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08080 Barcelona, Spain |
[1] |
Fei Yu, Kang Zuo. Weierstrass filtration on Teichmüller curves and Lyapunov exponents. Journal of Modern Dynamics, 2013, 7 (2) : 209-237. doi: 10.3934/jmd.2013.7.209 |
[2] |
Lucas Backes, Aaron Brown, Clark Butler. Continuity of Lyapunov exponents for cocycles with invariant holonomies. Journal of Modern Dynamics, 2018, 12: 223-260. doi: 10.3934/jmd.2018009 |
[3] |
Leonardo Mora. Homoclinic bifurcations, fat attractors and invariant curves. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1133-1148. doi: 10.3934/dcds.2003.9.1133 |
[4] |
Carlos H. Vásquez. Stable ergodicity for partially hyperbolic attractors with positive central Lyapunov exponents. Journal of Modern Dynamics, 2009, 3 (2) : 233-251. doi: 10.3934/jmd.2009.3.233 |
[5] |
Matthias Rumberger. Lyapunov exponents on the orbit space. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 91-113. doi: 10.3934/dcds.2001.7.91 |
[6] |
Edson de Faria, Pablo Guarino. Real bounds and Lyapunov exponents. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 1957-1982. doi: 10.3934/dcds.2016.36.1957 |
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Zoltán Buczolich, Gabriella Keszthelyi. Isentropes and Lyapunov exponents. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 1989-2009. doi: 10.3934/dcds.2020102 |
[8] |
Andy Hammerlindl. Integrability and Lyapunov exponents. Journal of Modern Dynamics, 2011, 5 (1) : 107-122. doi: 10.3934/jmd.2011.5.107 |
[9] |
Sebastian J. Schreiber. Expansion rates and Lyapunov exponents. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 433-438. doi: 10.3934/dcds.1997.3.433 |
[10] |
Fumihiko Nakamura, Yushi Nakano, Hisayoshi Toyokawa. Lyapunov exponents for random maps. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022058 |
[11] |
Àlex Haro. On strange attractors in a class of pinched skew products. Discrete and Continuous Dynamical Systems, 2012, 32 (2) : 605-617. doi: 10.3934/dcds.2012.32.605 |
[12] |
Antonio Pumariño, José Ángel Rodríguez, Enrique Vigil. Renormalizable Expanding Baker Maps: Coexistence of strange attractors. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1651-1678. doi: 10.3934/dcds.2017068 |
[13] |
Shin Kiriki, Yusuke Nishizawa, Teruhiko Soma. Heterodimensional tangencies on cycles leading to strange attractors. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 285-300. doi: 10.3934/dcds.2010.27.285 |
[14] |
Alexandre Rodrigues. "Large" strange attractors in the unfolding of a heteroclinic attractor. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2355-2379. doi: 10.3934/dcds.2021193 |
[15] |
Stefano Marò. Relativistic pendulum and invariant curves. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1139-1162. doi: 10.3934/dcds.2015.35.1139 |
[16] |
Yongluo Cao, Stefano Luzzatto, Isabel Rios. Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 61-71. doi: 10.3934/dcds.2006.15.61 |
[17] |
Shrihari Sridharan, Atma Ram Tiwari. The dependence of Lyapunov exponents of polynomials on their coefficients. Journal of Computational Dynamics, 2019, 6 (1) : 95-109. doi: 10.3934/jcd.2019004 |
[18] |
Chao Liang, Wenxiang Sun, Jiagang Yang. Some results on perturbations of Lyapunov exponents. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4287-4305. doi: 10.3934/dcds.2012.32.4287 |
[19] |
Alexandre A. Rodrigues. Rank-one strange attractors versus heteroclinic tangles. Communications on Pure and Applied Analysis, 2022, 21 (9) : 3213-3245. doi: 10.3934/cpaa.2022097 |
[20] |
Nguyen Dinh Cong, Thai Son Doan, Stefan Siegmund. On Lyapunov exponents of difference equations with random delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 861-874. doi: 10.3934/dcdsb.2015.20.861 |
2021 Impact Factor: 1.497
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