Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 24
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Carvalho, M. and Varandas, P. 2016. (Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms. Journal of Mathematical Analysis and Applications, Vol. 434, Issue. 2, p. 1123.

    Araujo, Vitor and Solano, Javier 2014. Absolutely continuous invariant measures for random non-uniformly expanding maps. Mathematische Zeitschrift, Vol. 277, Issue. 3-4, p. 1199.

    Varandas, Paulo 2014. Statistical properties of generalized Viana maps. Dynamical Systems, Vol. 29, Issue. 2, p. 167.

    VOLK, D. 2014. Persistent massive attractors of smooth maps. Ergodic Theory and Dynamical Systems, Vol. 34, Issue. 02, p. 679.

    ALVES, JOSÉ F. and VILARINHO, HELDER 2013. Strong stochastic stability for non-uniformly expanding maps. Ergodic Theory and Dynamical Systems, Vol. 33, Issue. 03, p. 647.

    Duan, Yuejiao 2013. ACIM for random intermittent maps: existence, uniqueness and stochastic stability. Dynamical Systems, Vol. 28, Issue. 1, p. 48.

    Gao, Rui and Shen, Weixiao 2013. Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps. Discrete and Continuous Dynamical Systems, Vol. 34, Issue. 5, p. 2013.

    Huang, Wen and Shen, Weixiao 2013. Analytic skew products of quadratic polynomials over circle expanding maps. Nonlinearity, Vol. 26, Issue. 2, p. 389.

    Solano, Javier 2013. Non-uniform hyperbolicity and existence of absolutely continuous invariant measures. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 44, Issue. 1, p. 67.

    Viana, Marcelo and Yang, Jiagang 2013. Physical measures and absolute continuity for one-dimensional center direction. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol. 30, Issue. 5, p. 845.

    Alves, José F and Soufi, Mohammad 2012. Statistical stability and limit laws for Rovella maps. Nonlinearity, Vol. 25, Issue. 12, p. 3527.

    Bahsoun, Wael and Vaienti, Sandro 2012. Metastability of certain intermittent maps. Nonlinearity, Vol. 25, Issue. 1, p. 107.

    Gianfelice, M. Maimone, F. Pelino, V. and Vaienti, S. 2012. On the Recurrence and Robust Properties of Lorenz’63 Model. Communications in Mathematical Physics, Vol. 313, Issue. 3, p. 745.

    Mesa, O. J. Gupta, V. K. and O'Connell, P. E. 2012. Extreme Events and Natural Hazards: The Complexity Perspective.

    Varandas, Paulo 2012. Non-uniform Specification and Large Deviations for Weak Gibbs Measures. Journal of Statistical Physics, Vol. 146, Issue. 2, p. 330.

    Alves, José F. Freitas, Jorge M. Luzzatto, Stefano and Vaienti, Sandro 2011. From rates of mixing to recurrence times via large deviations. Advances in Mathematics, Vol. 228, Issue. 2, p. 1203.

    Araújo, V. Castro, A. Pacifico, M.J. and Pinheiro, V. 2011. Multidimensional Rovella-like attractors. Journal of Differential Equations, Vol. 251, Issue. 11, p. 3163.

    Alves, José F. Carvalho, Maria and Freitas, Jorge Milhazes 2010. Statistical stability for Hénon maps of the Benedicks–Carleson type. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol. 27, Issue. 2, p. 595.

    GUPTA, CHINMAYA 2010. Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems. Ergodic Theory and Dynamical Systems, Vol. 30, Issue. 03, p. 757.

    Freitas, Jorge Milhazes and Todd, Mike 2009. The statistical stability of equilibrium states for interval maps. Nonlinearity, Vol. 22, Issue. 2, p. 259.


Statistical stability for robust classes of maps with non-uniform expansion

  • JOSÉ F. ALVES (a1) and MARCELO VIANA (a2)
  • DOI:
  • Published online: 01 January 2002

We consider open sets of transformations in a manifold M, exhibiting non-uniformly expanding behavior in some forward invariant domain U\subset M. Assuming that each transformation has a unique Sinai–Ruelle–Bowen (SRB) measure in U, and some general uniformity conditions, we prove that the SRB measure varies continuously with the dynamics in the L1-norm. We also describe a concrete application.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *