Building Expansion for Generalizations of Viana Maps

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2024-03-25 DOI:10.1007/s10884-024-10357-8

Vanderlei Horita, Nivaldo Muniz, Olivier Sester

引用次数: 0

Abstract

We study a family of skew-products of smooth functions having a unique critical point of degree \(D\ge 2\) over a strongly expanding map of the circle and prove that these systems admit two positive Lyapunov exponents. This extends an analogous result of Viana who considered, in the seminal paper (Viana in Inst Hautes Études Sci Publ Math 85:63–96, 1997), the quadratic case \(D=2\).

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维亚纳地图泛化的构建扩展

我们研究了在圆的强扩张映射上具有度 \(D\ge 2\) 唯一临界点的平滑函数的偏积族，并证明这些系统具有两个正的李亚普诺夫指数。这扩展了维亚纳的类似结果，维亚纳在开创性论文（维亚纳在高等研究院科学出版社数学85:63-96，1997）中考虑了二次情况\(D=2\)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.