Access the full text.
Sign up today, get DeepDyve free for 14 days.
E de Faria (2016)
1957Discrete Contin. Dyn. Syst. Ser. A, 36
G. Keller (1990)
Exponents, attractors and Hopf decompositions for interval mapsErgodic Theory and Dynamical Systems, 10
E. Faria, Pablo Guarino (2015)
Real bounds and Lyapunov exponentsDiscrete and Continuous Dynamical Systems, 36
F. Przytycki (1993)
Lyapunov characteristic exponents are nonnegative, 119
(2021)
Dynamics of Circle Mappings. 33 • Colóquio Brasileiro de Matemática
K. Khanin (1991)
Universal estimates for critical circle mappings.Chaos, 1 2
W de Melo, S van Strien (1993)
10.1007/978-3-642-78043-1One-Dimensional Dynamics
T. Nowicki, D. Sands (1998)
Non-uniform hyperbolicity and universal bounds for S-unimodal mapsInventiones mathematicae, 132
(1993)
Il n ’ y a pas de contre - exemple de Denjoy analytique
M. Tsujii (1993)
Positive Lyapunov exponents in families of one dimensional dynamical systemsInventiones mathematicae, 111
Michał Misiurewicz (2013)
ONE-DIMENSIONAL DYNAMICS
Edson Faria, Pablo Guarino (2020)
There are no σ-finite absolutely continuous invariant measures for multicritical circle mapsNonlinearity, 34
Simin Li, Qihan Wang (2013)
The slow recurrence and stochastic stability of unimodal interval maps with wild attractorsNonlinearity, 26
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
In this note we concern with the Lyapunov exponent for critical circle maps. We prove that for any C3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C^3$$\end{document} critical circle map with irrational rotation number, the Lyapunov exponent at x∈S1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$x \in S^1$$\end{document} equals 0 if and only if the orbit of x never hits the critical points. This implies that the Lyapunov exponent at the critical value for unicritical circle map with irrational rotation number is 0, which answers a question of de Faria and Guarino. The idea is to verify Tsujii’s slow recurrence condition.
"Bulletin of the Brazilian Mathematical Society, New Series" – Springer Journals
Published: Dec 1, 2022
Keywords: Lyapunov exponent; Circle map; Bounded geometry; Slow recurrence; 37E10; 37D25
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.