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Open problems in the theory of non-uniform hyperbolicity
1. | Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802, United States |
[1] |
Boris Kalinin, Anatole Katok. Measure rigidity beyond uniform hyperbolicity: invariant measures for cartan actions on tori. Journal of Modern Dynamics, 2007, 1 (1) : 123-146. doi: 10.3934/jmd.2007.1.123 |
[2] |
Grzegorz Łukaszewicz, James C. Robinson. Invariant measures for non-autonomous dissipative dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (10) : 4211-4222. doi: 10.3934/dcds.2014.34.4211 |
[3] |
Boris Kalinin, Anatole Katok, Federico Rodriguez Hertz. Errata to "Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori" and "Uniqueness of large invariant measures for $\Zk$ actions with Cartan homotopy data". Journal of Modern Dynamics, 2010, 4 (1) : 207-209. doi: 10.3934/jmd.2010.4.207 |
[4] |
Boris Hasselblatt, Yakov Pesin, Jörg Schmeling. Pointwise hyperbolicity implies uniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2819-2827. doi: 10.3934/dcds.2014.34.2819 |
[5] |
Pablo G. Barrientos, Abbas Fakhari. Ergodicity of non-autonomous discrete systems with non-uniform expansion. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1361-1382. doi: 10.3934/dcdsb.2019231 |
[6] |
Mickaël Kourganoff. Uniform hyperbolicity in nonflat billiards. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1145-1160. doi: 10.3934/dcds.2018048 |
[7] |
Miaohua Jiang. Derivative formula of the potential function for generalized SRB measures of hyperbolic systems of codimension one. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 967-983. doi: 10.3934/dcds.2015.35.967 |
[8] |
Xin Li, Wenxian Shen, Chunyou Sun. Invariant measures for complex-valued dissipative dynamical systems and applications. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2427-2446. doi: 10.3934/dcdsb.2017124 |
[9] |
Wael Bahsoun, Paweł Góra. SRB measures for certain Markov processes. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 17-37. doi: 10.3934/dcds.2011.30.17 |
[10] |
Dominic Veconi. SRB measures of singular hyperbolic attractors. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 3415-3430. doi: 10.3934/dcds.2022020 |
[11] |
Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087 |
[12] |
Michael Zgurovsky, Mark Gluzman, Nataliia Gorban, Pavlo Kasyanov, Liliia Paliichuk, Olha Khomenko. Uniform global attractors for non-autonomous dissipative dynamical systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 2053-2065. doi: 10.3934/dcdsb.2017120 |
[13] |
Jacques Demongeot, Dan Istrate, Hajer Khlaifi, Lucile Mégret, Carla Taramasco, René Thomas. From conservative to dissipative non-linear differential systems. An application to the cardio-respiratory regulation. Discrete and Continuous Dynamical Systems - S, 2020, 13 (8) : 2121-2134. doi: 10.3934/dcdss.2020181 |
[14] |
Péter Bálint, Imre Péter Tóth. Hyperbolicity in multi-dimensional Hamiltonian systems with applications to soft billiards. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 37-59. doi: 10.3934/dcds.2006.15.37 |
[15] |
David Damanik, Jake Fillman, Milivoje Lukic, William Yessen. Characterizations of uniform hyperbolicity and spectra of CMV matrices. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1009-1023. doi: 10.3934/dcdss.2016039 |
[16] |
Eleonora Catsigeras, Heber Enrich. SRB measures of certain almost hyperbolic diffeomorphisms with a tangency. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 177-202. doi: 10.3934/dcds.2001.7.177 |
[17] |
Marcin Mazur, Jacek Tabor, Piotr Kościelniak. Semi-hyperbolicity and hyperbolicity. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1029-1038. doi: 10.3934/dcds.2008.20.1029 |
[18] |
Raquel Ribeiro. Hyperbolicity and types of shadowing for $C^1$ generic vector fields. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2963-2982. doi: 10.3934/dcds.2014.34.2963 |
[19] |
Dawei Yang, Shaobo Gan, Lan Wen. Minimal non-hyperbolicity and index-completeness. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1349-1366. doi: 10.3934/dcds.2009.25.1349 |
[20] |
G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini. Time-dependent systems of generalized Young measures. Networks and Heterogeneous Media, 2007, 2 (1) : 1-36. doi: 10.3934/nhm.2007.2.1 |
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