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http://dx.doi.org/10.4134/JKMS.j170312

OPENNESS OF ANOSOV FAMILIES

Acevedo, Jeovanny de Jesus Muentes (Instituto de Matematica e Estatistica Universidade de Sao Paulo)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.3, 2018 , pp. 575-591 More about this Journal

Abstract

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of diffeomorphisms (or non-stationary dynamical system) with similar behavior to an Anosov diffeomorphisms. We show that the set consisting of Anosov families is an open subset of the set consisting of two-sided sequences of diffeomorphisms, which is equipped with the strong topology (or Whitney topology).

Keywords

Anosov families; Anosov diffeomorphism; random dynamical systems; non-stationary dynamical systems; non-autonomous dynamical systems;

Citations & Related Records

Reference

1	P. Arnoux and A. M. Fisher, Anosov families, renormalization and non-stationary subshifts, Ergodic Theory Dynam. Systems 25 (2005), no. 3, 661-709. DOI
2	V. I. Bakhtin, Random processes generated by a hyperbolic sequence of mappings. I, Russian Acad. Sci. Izv. Math. 44 (1995), no. 2, 247-279; translated from Izv. Ross. Akad. Nauk Ser. Mat. 58 (1994), no. 2, 40-72. DOI
3	V. I. Bakhtin, Random processes generated by a hyperbolic sequence of mappings. II, Russian Acad. Sci. Izv. Math. 44 (1995), no. 3, 617-627; translated from Izv. Ross. Akad. Nauk Ser. Mat. 58 (1994), no. 3, 184-195. DOI
4	L. Barreira and Y. Pesin, Nonuniform Hyperbolicity, Encyclopedia of Mathematics and its Applications, 115, Cambridge University Press, Cambridge, 2007.
5	P.-D. Liu, Random perturbations of Axiom A basic sets, J. Statist. Phys. 90 (1998), no. 1-2, 467-490. DOI
6	J. Muentes, Local Stable and Unstable Manifolds for Anosov Families, arXiv preprint arXiv:1709.00636.
7	J. Muentes, On the continuity of the topological entropy of non-autonomous dynamical systems, Bulletin of the Brazilian Mathematical Society, New Series (2017), 1-18.
8	J. Muentes, Structural Stability of Anosov Families, arXiv preprint arXiv:1709.00638.
9	M. Stenlund, Non-stationary compositions of Anosov diffeomorphisms, Nonlinearity 24 (2011), no. 10, 2991-3018. DOI
10	M. Shub, Global Stability of Dynamical Systems, translated from the French by Joseph Christy, Springer-Verlag, New York, 1987.
11	M. Viana, Lectures on Lyapunov Exponents, Cambridge Studies in Advanced Mathematics, 145, Cambridge University Press, Cambridge, 2014.
12	L.-S. Young, Stochastic stability of hyperbolic attractors, Ergodic Theory Dynam. Systems 6 (1986), no. 2, 311-319.