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A dynamical approach to von Neumann dimension
On the distribution of periodic orbits
1.  IMPA, Estrada Dona Castorina 110, Rio de Janeiro, RJ 22460320, Brazil 
2.  Department of Mathematics, Wichita State University, Wichita, Kansas, 67260 
[1] 
F. Rodriguez Hertz, M. A. Rodriguez Hertz, A. Tahzibi and R. Ures. A criterion for ergodicity for nonuniformly hyperbolic diffeomorphisms. Electronic Research Announcements, 2007, 14: 7481. doi: 10.3934/era.2007.14.74 
[2] 
Carlos Matheus, Jacob Palis. An estimate on the Hausdorff dimension of stable sets of nonuniformly hyperbolic horseshoes. Discrete & Continuous Dynamical Systems  A, 2018, 38 (2) : 431448. doi: 10.3934/dcds.2018020 
[3] 
José F. Alves. Nonuniformly expanding dynamics: Stability from a probabilistic viewpoint. Discrete & Continuous Dynamical Systems  A, 2001, 7 (2) : 363375. doi: 10.3934/dcds.2001.7.363 
[4] 
Xueting Tian, Paulo Varandas. Topological entropy of level sets of empirical measures for nonuniformly expanding maps. Discrete & Continuous Dynamical Systems  A, 2017, 37 (10) : 54075431. doi: 10.3934/dcds.2017235 
[5] 
Mark Pollicott. Local Hölder regularity of densities and Livsic theorems for nonuniformly hyperbolic diffeomorphisms. Discrete & Continuous Dynamical Systems  A, 2005, 13 (5) : 12471256. doi: 10.3934/dcds.2005.13.1247 
[6] 
Nicolai T. A. Haydn, Kasia Wasilewska. Limiting distribution and error terms for the number of visits to balls in nonuniformly hyperbolic dynamical systems. Discrete & Continuous Dynamical Systems  A, 2016, 36 (5) : 25852611. doi: 10.3934/dcds.2016.36.2585 
[7] 
Marzie Zaj, Abbas Fakhari, Fatemeh Helen Ghane, Azam Ehsani. Physical measures for certain class of nonuniformly hyperbolic endomorphisms on the solid torus. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 17771807. doi: 10.3934/dcds.2018073 
[8] 
DeJun Feng, Antti Käenmäki. Equilibrium states of the pressure function for products of matrices. Discrete & Continuous Dynamical Systems  A, 2011, 30 (3) : 699708. doi: 10.3934/dcds.2011.30.699 
[9] 
Rua Murray. Ulam's method for some nonuniformly expanding maps. Discrete & Continuous Dynamical Systems  A, 2010, 26 (3) : 10071018. doi: 10.3934/dcds.2010.26.1007 
[10] 
Alexander Arbieto, Luciano Prudente. Uniqueness of equilibrium states for some partially hyperbolic horseshoes. Discrete & Continuous Dynamical Systems  A, 2012, 32 (1) : 2740. doi: 10.3934/dcds.2012.32.27 
[11] 
Masayuki Asaoka, Kenichiro Yamamoto. On the large deviation rates of nonentropyapproachable measures. Discrete & Continuous Dynamical Systems  A, 2013, 33 (10) : 44014410. doi: 10.3934/dcds.2013.33.4401 
[12] 
José F. Alves. A survey of recent results on some statistical features of nonuniformly expanding maps. Discrete & Continuous Dynamical Systems  A, 2006, 15 (1) : 120. doi: 10.3934/dcds.2006.15.1 
[13] 
Jose F. Alves; Stefano Luzzatto and Vilton Pinheiro. Markov structures for nonuniformly expanding maps on compact manifolds in arbitrary dimension. Electronic Research Announcements, 2003, 9: 2631. 
[14] 
Hartmut Schwetlick, Daniel C. Sutton, Johannes Zimmer. On the $\Gamma$limit for a nonuniformly bounded sequence of twophase metric functionals. Discrete & Continuous Dynamical Systems  A, 2015, 35 (1) : 411426. doi: 10.3934/dcds.2015.35.411 
[15] 
Dongkui Ma, Min Wu. Topological pressure and topological entropy of a semigroup of maps. Discrete & Continuous Dynamical Systems  A, 2011, 31 (2) : 545556. doi: 10.3934/dcds.2011.31.545 
[16] 
Yueling Li, Yingchao Xie, Xicheng Zhang. Large deviation principle for stochastic heat equation with memory. Discrete & Continuous Dynamical Systems  A, 2015, 35 (11) : 52215237. doi: 10.3934/dcds.2015.35.5221 
[17] 
Christian Bonatti, Sylvain Crovisier, Katsutoshi Shinohara. The $C^{1+\alpha }$ hypothesis in Pesin Theory revisited. Journal of Modern Dynamics, 2013, 7 (4) : 605618. doi: 10.3934/jmd.2013.7.605 
[18] 
Bin Chen, Xiongping Dai. On uniformly recurrent motions of topological semigroup actions. Discrete & Continuous Dynamical Systems  A, 2016, 36 (6) : 29312944. doi: 10.3934/dcds.2016.36.2931 
[19] 
Marc Rauch. Variational principles for the topological pressure of measurable potentials. Discrete & Continuous Dynamical Systems  S, 2017, 10 (2) : 367394. doi: 10.3934/dcdss.2017018 
[20] 
Xueting Tian. Topological pressure for the completely irregular set of birkhoff averages. Discrete & Continuous Dynamical Systems  A, 2017, 37 (5) : 27452763. doi: 10.3934/dcds.2017118 
2016 Impact Factor: 1.099
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