-
Previous Article
Attractors for differential equations with multiple variable delays
- DCDS Home
- This Issue
-
Next Article
Semigroup representations in holomorphic dynamics
Entropy of endomorphisms of Lie groups
1. | Departamento de Matemática, Universidade de Brasília, Campus Darcy Ribeiro, Cx. Postal 4481, Brasília-DF, 70.904-970, Brazil |
References:
[1] |
F. Blanchard, E. Glasner, S. Kolyada and A. Maas, On Li-Yorke pairs, J. Reine Angew. Math., 547 (2002), 51-68. |
[2] |
R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Americ. Math Soc., 153 (1971), 401-414.
doi: 10.1090/S0002-9947-1971-0274707-X. |
[3] |
T. Ferraiol, "Entropia e Ações de Grupos de Lie," Master thesis, University of Campinas, 2008. |
[4] |
T. Ferraiol, M. Patrão and L. Seco, Jordan decomposition and dynamics on flag manifolds, Discrete Contin. Dyn. Syst. A, 26 (2010), 923-947.
doi: 10.3934/dcds.2010.26.923. |
[5] |
E. Glasner, A simple characterization of the set of $\mu$-entropy pairs and applications, Isr. J. Math., 102 (1997), 13-27.
doi: 10.1007/BF02773793. |
[6] |
M. Handel and B. Kitchens, Metrics and entropy for non-compact spaces, Isr. J. Math., 91 (1995), 253-271.
doi: 10.1007/BF02761650. |
[7] |
S. Helgason, "Differential Geometry, Lie Groups and Symmetric Spaces," Academic Press, New York, 1978. |
[8] |
A. W. Knapp, "Lie Groups Beyond an Introduction," Progress in Mathematics, 140, Birkhäuser, Boston, 2002. |
[9] |
M. Patrão, Entropy and its Variational Principle for Non-Compact Metric Spaces, Ergodic Theory and Dynamical Systems, 30 (2010), 1529-1542.
doi: 10.1017/S0143385709000674. |
[10] |
M. Patrão, L. Santos and L. Seco, A Note on the Jordan Decomposition, Proyecciones Journal of Mathematics, 30 (2011), 123-136.
doi: 10.4067/S0716-09172011000100011. |
[11] |
Ya. G. Sinai, On the Notion of Entropy of a Dynamical System, Doklady of Russian Academy of Sciences, 124 (1959), 768-771. |
show all references
References:
[1] |
F. Blanchard, E. Glasner, S. Kolyada and A. Maas, On Li-Yorke pairs, J. Reine Angew. Math., 547 (2002), 51-68. |
[2] |
R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Americ. Math Soc., 153 (1971), 401-414.
doi: 10.1090/S0002-9947-1971-0274707-X. |
[3] |
T. Ferraiol, "Entropia e Ações de Grupos de Lie," Master thesis, University of Campinas, 2008. |
[4] |
T. Ferraiol, M. Patrão and L. Seco, Jordan decomposition and dynamics on flag manifolds, Discrete Contin. Dyn. Syst. A, 26 (2010), 923-947.
doi: 10.3934/dcds.2010.26.923. |
[5] |
E. Glasner, A simple characterization of the set of $\mu$-entropy pairs and applications, Isr. J. Math., 102 (1997), 13-27.
doi: 10.1007/BF02773793. |
[6] |
M. Handel and B. Kitchens, Metrics and entropy for non-compact spaces, Isr. J. Math., 91 (1995), 253-271.
doi: 10.1007/BF02761650. |
[7] |
S. Helgason, "Differential Geometry, Lie Groups and Symmetric Spaces," Academic Press, New York, 1978. |
[8] |
A. W. Knapp, "Lie Groups Beyond an Introduction," Progress in Mathematics, 140, Birkhäuser, Boston, 2002. |
[9] |
M. Patrão, Entropy and its Variational Principle for Non-Compact Metric Spaces, Ergodic Theory and Dynamical Systems, 30 (2010), 1529-1542.
doi: 10.1017/S0143385709000674. |
[10] |
M. Patrão, L. Santos and L. Seco, A Note on the Jordan Decomposition, Proyecciones Journal of Mathematics, 30 (2011), 123-136.
doi: 10.4067/S0716-09172011000100011. |
[11] |
Ya. G. Sinai, On the Notion of Entropy of a Dynamical System, Doklady of Russian Academy of Sciences, 124 (1959), 768-771. |
[1] |
Ghassen Askri. Li-Yorke chaos for dendrite maps with zero topological entropy and ω-limit sets. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 2957-2976. doi: 10.3934/dcds.2017127 |
[2] |
Jakub Šotola. Relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 5119-5128. doi: 10.3934/dcds.2018225 |
[3] |
Daniel Gonçalves, Bruno Brogni Uggioni. Li-Yorke Chaos for ultragraph shift spaces. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2347-2365. doi: 10.3934/dcds.2020117 |
[4] |
Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $ \beta $-transformation. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 525-536. doi: 10.3934/dcds.2020267 |
[5] |
Adriano Da Silva, Alexandre J. Santana, Simão N. Stelmastchuk. Topological conjugacy of linear systems on Lie groups. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3411-3421. doi: 10.3934/dcds.2017144 |
[6] |
Paul Skerritt, Cornelia Vizman. Dual pairs for matrix groups. Journal of Geometric Mechanics, 2019, 11 (2) : 255-275. doi: 10.3934/jgm.2019014 |
[7] |
Javier Pérez Álvarez. Invariant structures on Lie groups. Journal of Geometric Mechanics, 2020, 12 (2) : 141-148. doi: 10.3934/jgm.2020007 |
[8] |
Gerard Thompson. Invariant metrics on Lie groups. Journal of Geometric Mechanics, 2015, 7 (4) : 517-526. doi: 10.3934/jgm.2015.7.517 |
[9] |
Min Qian, Jian-Sheng Xie. Entropy formula for endomorphisms: Relations between entropy, exponents and dimension. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 367-392. doi: 10.3934/dcds.2008.21.367 |
[10] |
Benjamin Weiss. Entropy and actions of sofic groups. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3375-3383. doi: 10.3934/dcdsb.2015.20.3375 |
[11] |
Katrin Gelfert. Lower bounds for the topological entropy. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 555-565. doi: 10.3934/dcds.2005.12.555 |
[12] |
Jaume Llibre. Brief survey on the topological entropy. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3363-3374. doi: 10.3934/dcdsb.2015.20.3363 |
[13] |
Isaac A. García, Jaume Giné, Jaume Llibre. Liénard and Riccati differential equations related via Lie Algebras. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 485-494. doi: 10.3934/dcdsb.2008.10.485 |
[14] |
M. P. de Oliveira. On 3-graded Lie algebras, Jordan pairs and the canonical kernel function. Electronic Research Announcements, 2003, 9: 142-151. |
[15] |
Dongkui Ma, Min Wu. Topological pressure and topological entropy of a semigroup of maps. Discrete and Continuous Dynamical Systems, 2011, 31 (2) : 545-557 . doi: 10.3934/dcds.2011.31.545 |
[16] |
Piotr Oprocha, Paweł Potorski. Topological mixing, knot points and bounds of topological entropy. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3547-3564. doi: 10.3934/dcdsb.2015.20.3547 |
[17] |
Richard Sharp. Distortion and entropy for automorphisms of free groups. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 347-363. doi: 10.3934/dcds.2010.26.347 |
[18] |
Boris Hasselblatt, Zbigniew Nitecki, James Propp. Topological entropy for nonuniformly continuous maps. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 201-213. doi: 10.3934/dcds.2008.22.201 |
[19] |
Michał Misiurewicz. On Bowen's definition of topological entropy. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 827-833. doi: 10.3934/dcds.2004.10.827 |
[20] |
Lluís Alsedà, David Juher, Francesc Mañosas. Forward triplets and topological entropy on trees. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 623-641. doi: 10.3934/dcds.2021131 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]