Markov structures and decay of correlations for non-uniformly expanding dynamical systems
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 817-839. 
@article{AIHPC_2005__22_6_817_0,
     author = {Alves, Jos\'e F. and Luzzatto, Stefano and Pinheiro, Vilton},
     title = {Markov structures and decay of correlations for non-uniformly expanding dynamical systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {817--839},
     publisher = {Elsevier},
     volume = {22},
     number = {6},
     year = {2005},
     doi = {10.1016/j.anihpc.2004.12.002},
     mrnumber = {2172861},
     zbl = {02245288},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/}
}
TY  - JOUR
AU  - Alves, José F.
AU  - Luzzatto, Stefano
AU  - Pinheiro, Vilton
TI  - Markov structures and decay of correlations for non-uniformly expanding dynamical systems
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2005
SP  - 817
EP  - 839
VL  - 22
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/
DO  - 10.1016/j.anihpc.2004.12.002
LA  - en
ID  - AIHPC_2005__22_6_817_0
ER  - 
%0 Journal Article
%A Alves, José F.
%A Luzzatto, Stefano
%A Pinheiro, Vilton
%T Markov structures and decay of correlations for non-uniformly expanding dynamical systems
%J Annales de l'I.H.P. Analyse non linéaire
%D 2005
%P 817-839
%V 22
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/
%R 10.1016/j.anihpc.2004.12.002
%G en
%F AIHPC_2005__22_6_817_0
Alves, José F.; Luzzatto, Stefano; Pinheiro, Vilton. Markov structures and decay of correlations for non-uniformly expanding dynamical systems. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 817-839. doi : 10.1016/j.anihpc.2004.12.002. https://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/

[1] Alves J.F., SRB measures for non-hyperbolic systems with multidimensional expansion, Ann. Sci. École Norm. Sup. 33 (4) (2000) 1-32. | Numdam | MR | Zbl

[2] Alves J.F., Araújo V., Random perturbations of nonuniformly expanding maps, Astérisque 286 (2003) 25-62. | Numdam | MR | Zbl

[3] Alves J.F., Bonatti C., Viana M., SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math. 140 (2000) 351-398. | MR | Zbl

[4] Alves J.F., Luzzatto S., Pinheiro V., Lyapunov exponent and rates of mixing for one-dimensional maps, Ergodic Theory Dynam. Systems 24 (2004) 637-657. | MR | Zbl

[5] Alves J.F., Viana M., Statistical stability for robust classes of maps with non-uniform expansion, Ergodic Theory Dynam. Systems 22 (2002) 1-32. | MR | Zbl

[6] Adler R., Weiss B., Proc. Entropy, a complete metric invariant for automorphisms of the torus, Nat. Acad. Sci. USA 57 (1967) 1573-1576. | MR | Zbl

[7] Adler R., Weiss B., Similarity of Automorphisms of the Torus, Mem. Amer. Math. Soc., vol. 98, Amer. Math. Soc., Providence, RI, 1970. | MR | Zbl

[8] V. Baladi, M. Benedicks, V. Maume-Deschamps, Almost sure rate of mixing for i.i.d unimodal maps, Ann. Sci. Écol. Norm. Sup. (4) (2002). | Numdam | MR | Zbl

[9] Bruin H., Luzzatto S., Van Strien S., Rates of decay of correlations in one-dimensional dynamics, Ann. Sci. Écol. Norm. Sup. 36 (2003) 621-646. | Numdam | MR | Zbl

[10] Bowen R., Ruelle D., The ergodic theory of Axiom A flows, Invent. Math. 29 (1975) 181-202. | MR | Zbl

[11] Bowen R., Markov partitions for Axiom diffeomorphisms, Amer. J. Math. 92 (1970) 725-747. | MR | Zbl

[12] Bowen R., Equilibrium States and the Ergodic Theory of Axiom A Diffeomorphisms, Lecture Notes in Math., vol. 92, Springer, 1975. | MR | Zbl

[13] Bressaud X., Subshifts on an infinite alphabet, Ergodic Theory Dynam. Systems 19 (5) (1999) 1175-1200. | MR | Zbl

[14] Bunimovich L.A., Sinaĭ Ya.G., Chernov N.I., Statistical properties of two-dimensional hyperbolic billiards, Russian Math. Surveys 46 (4) (1991) 47-106. | MR | Zbl

[15] Buzzi J., Markov extensions for multi-dimensional dynamical systems, Israel J. Math. 112 (1999) 357-380. | MR | Zbl

[16] Buzzi J., Maume-Deschamps V., Decay of correlations for piecewise invertible maps in higher dimensions, Israel J. Math. 131 (2002) 203-220. | MR | Zbl

[17] J. Buzzi, V. Maume-Deschamps, Decay of correlations on towers with non-Hólder Jacobian and non-exponential return time, Preprint, 2002. | MR

[18] Buzzi J., Sester O., Tsujii M., Weakly expanding skew-products of quadratic maps, Ergodic Theory Dynam. Systems 24 (2004) 385-405. | MR | Zbl

[19] M. Holland, Slowly mixing systems and intermittency maps, Ergodic Theory Dynam. Systems, in press. | MR | Zbl

[20] Hu H., Decay of correlations for piecewise smooth maps with indifferent fixed points, Ergodic Theory Dynam. Systems 24 (2004) 495-524. | MR | Zbl

[21] Krüger T., Troubetzkoy S., Markov partitions and shadowing for non-uniformly hyperbolic systems with singularitie, Ergodic Theory Dynam. Systems 12 (3) (1992) 487-508. | MR | Zbl

[22] Liverani C., Saussol B., Vaienti S., A probabilistic approach to intermittancy, Ergodic Theory Dynam. Systems 19 (1999) 671-685. | MR | Zbl

[23] Maume-Deschamps V., Correlation decay for Markov maps on a countable state space, Ergodic Theory Dynam. Systems 21 (2001) 165-196. | MR | Zbl

[24] Pollicott M., Yuri M., Statistical properties of maps with indifferent periodic points, Commun. Math. Phys. 217 (2001) 503-520. | MR | Zbl

[25] Sarig O., Thermodynamical formalism for countable Markov shifts, Ergodic Theory Dynam. Systems 19 (1999) 1565-1593. | MR | Zbl

[26] Sarig O., Subexponential decay of correlations, Invent. Math. 150 (2002) 629-653. | MR | Zbl

[27] Sinai Y., Markov partitions and U-diffeomorphisms, Funktsional Anal. i Prilozhen. 32 (2) (1968) 70-80. | MR | Zbl

[28] Viana M., Multidimensional non-hyperbolic attractors, Publ. Math. IHES 85 (1997) 63-96. | Numdam | Zbl

[29] Young L.-S., Statistical properties of dynamical systems with some hyperbolicity, Ann. Math. 147 (1998) 585-650. | MR | Zbl

[30] Young L.-S., Recurrence times and rates of mixing, Israel J. Math. 110 (1999) 153-188. | MR | Zbl

[31] Yuri M., On the speed of convergence to equilibrium states for multi-dimensional maps with indifferent fixed points, Nonlinearity 15 (2002) 429-445. | MR | Zbl

  • Melbourne, Ian; Varandas, Paulo Good Inducing Schemes for Uniformly Hyperbolic Flows, and Applications to Exponential Decay of Correlations, Annales Henri Poincaré, Volume 26 (2025) no. 3, p. 921 | DOI:10.1007/s00023-024-01439-w
  • Chicalé, Ricardo; Horita, Vanderlei Invariant Measures of Non-uniformly Expanding Maps with Higher Order Critical Set, Journal of Dynamics and Differential Equations (2025) | DOI:10.1007/s10884-025-10417-7
  • Coates, Douglas; Luzzatto, Stefano Persistent Non-statistical Dynamics in One-Dimensional Maps, Communications in Mathematical Physics, Volume 405 (2024) no. 4 | DOI:10.1007/s00220-024-04957-0
  • Takahasi, Hiroki Exponential Mixing for Heterochaos Baker Maps and the Dyck System, Journal of Dynamics and Differential Equations (2024) | DOI:10.1007/s10884-024-10370-x
  • Araujo, Ermerson; Lima, Yuri; Poletti, Mauricio Symbolic Dynamics for Nonuniformly Hyperbolic Maps with Singularities in High Dimension, Memoirs of the American Mathematical Society, Volume 301 (2024) no. 1511 | DOI:10.1090/memo/1511
  • Araújo, Vitor; Trindade, Edvan Robust Exponential Mixing and Convergence to Equilibrium for Singular-Hyperbolic Attracting Sets, Journal of Dynamics and Differential Equations, Volume 35 (2023) no. 3, p. 2487 | DOI:10.1007/s10884-021-10100-7
  • Berry, Tyrus; Das, Suddhasattwa Learning Theory for Dynamical Systems, SIAM Journal on Applied Dynamical Systems, Volume 22 (2023) no. 3, p. 2082 | DOI:10.1137/22m1516865
  • Castorrini, Roberto; Liverani, Carlangelo Quantitative statistical properties of two-dimensional partially hyperbolic systems, Advances in Mathematics, Volume 409 (2022), p. 108625 | DOI:10.1016/j.aim.2022.108625
  • Climenhaga, Vaughn; Luzzatto, Stefano; Pesin, Yakov SRB Measures and Young Towers for Surface Diffeomorphisms, Annales Henri Poincaré, Volume 23 (2022) no. 3, p. 973 | DOI:10.1007/s00023-021-01113-5
  • Alves, José F.; Bahsoun, Wael; Ruziboev, Marks Almost sure rates of mixing for partially hyperbolic attractors, Journal of Differential Equations, Volume 311 (2022), p. 98 | DOI:10.1016/j.jde.2021.12.008
  • Bruin, Henk; Melbourne, Ian; Terhesiu, Dalia Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards, Annales Henri Lebesgue, Volume 4 (2021), p. 407 | DOI:10.5802/ahl.76
  • CRUZ, ANDERSON; VARANDAS, PAULO SRB measures for partially hyperbolic attractors of local diffeomorphisms, Ergodic Theory and Dynamical Systems, Volume 40 (2020) no. 6, p. 1545 | DOI:10.1017/etds.2018.115
  • Alves, José F. Introduction, Nonuniformly Hyperbolic Attractors (2020), p. 1 | DOI:10.1007/978-3-030-62814-7_1
  • Alves, José F. Nonuniformly Expanding Attractors, Nonuniformly Hyperbolic Attractors (2020), p. 189 | DOI:10.1007/978-3-030-62814-7_6
  • Araújo, V.; Melbourne, I. Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation, Advances in Mathematics, Volume 349 (2019), p. 212 | DOI:10.1016/j.aim.2019.04.007
  • Araujo, Vitor; Souza, Andressa; Trindade, Edvan Upper Large Deviations Bound for Singular-Hyperbolic Attracting Sets, Journal of Dynamics and Differential Equations, Volume 31 (2019) no. 2, p. 601 | DOI:10.1007/s10884-018-9723-6
  • Chevyrev, Ilya; Friz, Peter K.; Korepanov, Alexey; Melbourne, Ian; Zhang, Huilin Multiscale Systems, Homogenization, and Rough Paths, Probability and Analysis in Interacting Physical Systems, Volume 283 (2019), p. 17 | DOI:10.1007/978-3-030-15338-0_2
  • Korepanov, A.; Kosloff, Z.; Melbourne, I. Martingale–coboundary decomposition for families of dynamical systems, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 35 (2018) no. 4, p. 859 | DOI:10.1016/j.anihpc.2017.08.005
  • Capett-Figueras, Pedro L.; Sánchez-Salas, Fernando J. Yet another induction scheme for non-uniformly expanding transformations, Journal of Mathematical Analysis and Applications, Volume 466 (2018) no. 1, p. 281 | DOI:10.1016/j.jmaa.2018.05.073
  • Bálint, Péter; Melbourne, Ian Statistical Properties for Flows with Unbounded Roof Function, Including the Lorenz Attractor, Journal of Statistical Physics, Volume 172 (2018) no. 4, p. 1101 | DOI:10.1007/s10955-018-2093-y
  • Climenhaga, Vaughn; Pesin, Yakov Building Thermodynamics for Non-uniformly Hyperbolic Maps, Arnold Mathematical Journal, Volume 3 (2017) no. 1, p. 37 | DOI:10.1007/s40598-016-0052-8
  • de Simoi, Jacopo; Liverani, Carlangelo; Poquet, Christophe; Volk, Denis Fast–Slow Partially Hyperbolic Systems Versus Freidlin–Wentzell Random Systems, Journal of Statistical Physics, Volume 166 (2017) no. 3-4, p. 650 | DOI:10.1007/s10955-016-1628-3
  • Li, Xin Local Gibbs–Markov–Young structures for non-invertible systems, Dynamical Systems, Volume 31 (2016) no. 3, p. 311 | DOI:10.1080/14689367.2015.1114592
  • De Simoi, Jacopo; Liverani, Carlangelo Statistical properties of mostly contracting fast-slow partially hyperbolic systems, Inventiones mathematicae, Volume 206 (2016) no. 1, p. 147 | DOI:10.1007/s00222-016-0651-y
  • Li, Denghui; Chen, Hebai; Xie, Jianhua Statistical properties of the universal limit map of grazing bifurcations, Journal of Physics A: Mathematical and Theoretical, Volume 49 (2016) no. 35, p. 355102 | DOI:10.1088/1751-8113/49/35/355102
  • Marzen, Sarah E.; Crutchfield, James P. Statistical signatures of structural organization: The case of long memory in renewal processes, Physics Letters A, Volume 380 (2016) no. 17, p. 1517 | DOI:10.1016/j.physleta.2016.02.052
  • Alves, José F.; Li, Xin Gibbs–Markov–Young structures with (stretched) exponential tail for partially hyperbolic attractors, Advances in Mathematics, Volume 279 (2015), p. 405 | DOI:10.1016/j.aim.2015.02.017
  • Luzzatto, Stefano; Ruziboev, Marks Young towers for product systems, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 3, p. 1465 | DOI:10.3934/dcds.2016.36.1465
  • Varandas, Paulo Statistical properties of generalized Viana maps, Dynamical Systems, Volume 29 (2014) no. 2, p. 167 | DOI:10.1080/14689367.2013.868868
  • Bose, Christopher; Murray, Rua First hyperbolic times for intermittent maps with unbounded derivative, Dynamical Systems, Volume 29 (2014) no. 3, p. 352 | DOI:10.1080/14689367.2014.902038
  • Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives, International Journal of Bifurcation and Chaos, Volume 24 (2014) no. 10, p. 1430028 | DOI:10.1142/s0218127414300286
  • Araujo, Vitor; Pacifico, Maria Jose; Pinheiro, Mariana Adapted random perturbations for non-uniformly expanding maps, Stochastics and Dynamics, Volume 14 (2014) no. 04, p. 1450007 | DOI:10.1142/s0219493714500075
  • Alves, José F.; Dias, Carla L.; Luzzatto, Stefano Geometry of expanding absolutely continuous invariant measures and the liftability problem, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 30 (2013) no. 1, p. 101 | DOI:10.1016/j.anihpc.2012.06.004
  • Viana, Marcelo; Yang, Jiagang Physical measures and absolute continuity for one-dimensional center direction, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 30 (2013) no. 5, p. 845 | DOI:10.1016/j.anihpc.2012.11.002
  • ALVES, JOSÉ F.; VILARINHO, HELDER Strong stochastic stability for non-uniformly expanding maps, Ergodic Theory and Dynamical Systems, Volume 33 (2013) no. 3, p. 647 | DOI:10.1017/s0143385712000077
  • BOSE, CHRISTOPHER; MURRAY, RUA POLYNOMIAL DECAY OF CORRELATIONS IN THE GENERALIZED BAKER'S TRANSFORMATION, International Journal of Bifurcation and Chaos, Volume 23 (2013) no. 08, p. 1350130 | DOI:10.1142/s0218127413501307
  • Benderskii, V.A.; Kotkin, A.S.; Kats, E.I. Revivals in Caldeira–Leggett Hamiltonian dynamics, Physics Letters A, Volume 377 (2013) no. 10-11, p. 737 | DOI:10.1016/j.physleta.2013.01.027
  • Fernández, J L; Melián, M V; Pestana, D Expanding maps, shrinking targets and hitting times, Nonlinearity, Volume 25 (2012) no. 9, p. 2443 | DOI:10.1088/0951-7715/25/9/2443
  • Alves, José F.; Freitas, Jorge M.; Luzzatto, Stefano; Vaienti, Sandro From rates of mixing to recurrence times via large deviations, Advances in Mathematics, Volume 228 (2011) no. 2, p. 1203 | DOI:10.1016/j.aim.2011.06.014
  • Pinheiro, Vilton Expanding measures, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 28 (2011) no. 6, p. 889 | DOI:10.1016/j.anihpc.2011.07.001
  • Araújo, V.; Castro, A.; Pacifico, M.J.; Pinheiro, V. Multidimensional Rovella-like attractors, Journal of Differential Equations, Volume 251 (2011) no. 11, p. 3163 | DOI:10.1016/j.jde.2011.07.021
  • Alves, José F.; Pinheiro, Vilton Gibbs–Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction, Advances in Mathematics, Volume 223 (2010) no. 5, p. 1706 | DOI:10.1016/j.aim.2009.10.010
  • Gupta, Chinmaya; Nicol, Matthew; Ott, William A Borel–Cantelli lemma for nonuniformly expanding dynamical systems, Nonlinearity, Volume 23 (2010) no. 8, p. 1991 | DOI:10.1088/0951-7715/23/8/010
  • Freitas, Ana Cristina Moreira; Freitas, Jorge Milhazes; Todd, Mike Hitting time statistics and extreme value theory, Probability Theory and Related Fields, Volume 147 (2010) no. 3-4, p. 675 | DOI:10.1007/s00440-009-0221-y
  • Gouëzel, Sébastien Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences, Duke Mathematical Journal, Volume 147 (2009) no. 2 | DOI:10.1215/00127094-2009-011
  • Artuso, Roberto; Manchein, Cesar Instability statistics and mixing rates, Physical Review E, Volume 80 (2009) no. 3 | DOI:10.1103/physreve.80.036210
  • Baladi, Viviane Linear response despite critical points, Nonlinearity, Volume 21 (2008) no. 6, p. T81 | DOI:10.1088/0951-7715/21/6/t01
  • Chazottes, J.-R.; Gouëzel, S. On almost-sure versions of classical limit theorems for dynamical systems, Probability Theory and Related Fields, Volume 138 (2007) no. 1-2, p. 195 | DOI:10.1007/s00440-006-0021-6
  • Alves, José F.; Oliveira, Krerley; Tahzibi, Ali On the Continuity of the SRB Entropy for Endomorphisms, Journal of Statistical Physics, Volume 123 (2006) no. 4, p. 763 | DOI:10.1007/s10955-006-9059-1
  • Araújo, V.; Pacifico, M. J. Large Deviations for Non-Uniformly Expanding Maps, Journal of Statistical Physics, Volume 125 (2006) no. 2, p. 411 | DOI:10.1007/s10955-006-9183-y
  • Pinheiro, Vilton Sinai–Ruelle–Bowen measures for weakly expanding maps, Nonlinearity, Volume 19 (2006) no. 5, p. 1185 | DOI:10.1088/0951-7715/19/5/008
  • DÍAZ-ORDAZ, K.; HOLLAND, M. P.; LUZZATTO, S. STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS WITH CRITICAL POINTS AND SINGULARITIES, Stochastics and Dynamics, Volume 06 (2006) no. 04, p. 423 | DOI:10.1142/s0219493706001852

Cité par 52 documents. Sources : Crossref