Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-06T15:47:12.198Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-continuous weakly expanding skew-products of quadratic maps with two positive Lyapunov exponents

Published online by Cambridge University Press:  01 February 2008

DANIEL SCHNELLMANN
DANIEL SCHNELLMANN*
Affiliation:
Royal Institute of Technology (KTH), Department of Mathematics, S-100 44 Stockholm, Sweden (email: dansch@math.kth.se)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study an extension of the Viana map where the base dynamics is a discontinuous expanding map, and prove the existence of two positive Lyapunov exponents.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 1 , February 2008 , pp. 245 - 266
Copyright
Copyright © Cambridge University Press 2007

References

[1]Alves, J. F.. SRB measures for non-hyperbolic systems with multidimensional expansion. Ann. Sci. École Norm. Sup. (4) 33(1) (2000), 1–32.CrossRefGoogle Scholar
[2]Alves, J. F., Bonatti, C. and Viana, M.. SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Invent. Math. 140 (2000), 351–398.CrossRefGoogle Scholar
[3]Alves, J. F. and Viana, M.. Statistical stability for robust classes of maps with non-uniform expansion. Ergod. Th. & Dynam. Sys. 22 (2002), 1–32.CrossRefGoogle Scholar
[4]Buzzi, J., Sester, O. and Tsujii, M.. Weakly expanding skew-products of quadratic maps. Ergod. Th. & Dynam. Sys. 23 (2003), 1401–1414.CrossRefGoogle Scholar
[5]de Melo, W. and van Strien, S.. One-Dimensional Dynamics. Springer, Berlin, 1993.CrossRefGoogle Scholar
[6]Parry, W.. On the β-expansion of real numbers. Acta Math. Acad. Sci. Hung. 11 (1960), 401–416.CrossRefGoogle Scholar
[7]Pliss, V. A.. On a conjecture due to Smale. Diff. Uravnenija 8 (1972), 268–282.Google Scholar
[8]Rényi, A.. Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hung. 8 (1957), 477–493.CrossRefGoogle Scholar
[9]Schmeling, J.. Symbolic dynamics for β-shifts and self-normal numbers. Ergod. Th. & Dynam. Sys. 17 (1997), 675–694.CrossRefGoogle Scholar
[10]Viana, M.. Multidimensional non-hyperbolic attractors. Inst. Hautes Etudes Sci. Publ. Math. 85 (1997), 63–96.CrossRefGoogle Scholar