American Institute of Mathematical Sciences

Anatole Katok, Federico Rodriguez Hertz. Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank abelian groups. Journal of Modern Dynamics, 2010, 4 (3) : 487-515. doi: 10.3934/jmd.2010.4.487

Danijela Damjanovic and Anatole Katok. Local rigidity of actions of higher rank abelian groups and KAM method. Electronic Research Announcements, 2004, 10: 142-154.

David Mieczkowski. The first cohomology of parabolic actions for some higher-rank abelian groups and representation theory. Journal of Modern Dynamics, 2007, 1 (1) : 61-92. doi: 10.3934/jmd.2007.1.61

H. Bercovici, V. Niţică. Cohomology of higher rank abelian Anosov actions for Banach algebra valued cocycles. Conference Publications, 2001, 2001 (Special) : 50-55. doi: 10.3934/proc.2001.2001.50

Anatole Katok, Federico Rodriguez Hertz. Arithmeticity and topology of smooth actions of higher rank abelian groups. Journal of Modern Dynamics, 2016, 10: 135-172. doi: 10.3934/jmd.2016.10.135

Felipe A. Ramírez. Cocycles over higher-rank abelian actions on quotients of semisimple Lie groups. Journal of Modern Dynamics, 2009, 3 (3) : 335-357. doi: 10.3934/jmd.2009.3.335

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

Salvatore Cosentino, Livio Flaminio. Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds. Journal of Modern Dynamics, 2015, 9: 305-353. doi: 10.3934/jmd.2015.9.305

Manfred Einsiedler, Elon Lindenstrauss. Symmetry of entropy in higher rank diagonalizable actions and measure classification. Journal of Modern Dynamics, 2018, 13: 163-185. doi: 10.3934/jmd.2018016

Danijela Damjanović. Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions. Journal of Modern Dynamics, 2007, 1 (4) : 665-688. doi: 10.3934/jmd.2007.1.665

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

Masayuki Asaoka. Local rigidity of homogeneous actions of parabolic subgroups of rank-one Lie groups. Journal of Modern Dynamics, 2015, 9: 191-201. doi: 10.3934/jmd.2015.9.191

Mao Okada. Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces. Journal of Modern Dynamics, 2021, 17: 111-143. doi: 10.3934/jmd.2021004

Federico Rodriguez Hertz. Global rigidity of certain Abelian actions by toral automorphisms. Journal of Modern Dynamics, 2007, 1 (3) : 425-442. doi: 10.3934/jmd.2007.1.425

Ethan M. Ackelsberg. Rigidity, weak mixing, and recurrence in abelian groups. Discrete and Continuous Dynamical Systems, 2022, 42 (4) : 1669-1705. doi: 10.3934/dcds.2021168

Andrei Török. Rigidity of partially hyperbolic actions of property (T) groups. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 193-208. doi: 10.3934/dcds.2003.9.193

Minsung Kim. Limit theorems for higher rank actions on Heisenberg nilmanifolds. Discrete and Continuous Dynamical Systems, 2022  doi: 10.3934/dcds.2022057

Luis Barreira, Claudia Valls. Growth rates and nonuniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 509-528. doi: 10.3934/dcds.2008.22.509

Jana Rodriguez Hertz. Genericity of nonuniform hyperbolicity in dimension 3. Journal of Modern Dynamics, 2012, 6 (1) : 121-138. doi: 10.3934/jmd.2012.6.121

Yakov Pesin. On the work of Dolgopyat on partial and nonuniform hyperbolicity. Journal of Modern Dynamics, 2010, 4 (2) : 227-241. doi: 10.3934/jmd.2010.4.227