New Derived from Anosov Diffeomorphisms with Pathological Center Foliation
| Autor: | F. Micena |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematics::Dynamical Systems
Dynamical Systems (math.DS) Lyapunov exponent 01 natural sciences Combinatorics symbols.namesake 0502 economics and business FOS: Mathematics Almost everywhere Mathematics - Dynamical Systems 0101 mathematics Mathematics::Symplectic Geometry Mathematics 010102 general mathematics 05 social sciences Mathematical analysis Center (category theory) Torus Absolute continuity Automorphism Mathematics::Geometric Topology Foliation symbols Diffeomorphism 050203 business & management Analysis |
| Zdroj: | Journal of Dynamics and Differential Equations. 29:1159-1172 |
| ISSN: | 1572-9222 1040-7294 |
| DOI: | 10.1007/s10884-016-9523-9 |
| Popis: | In this paper we focused our study on derived from Anosov diffeomorphisms (DA diffeomorphisms ) of the torus \(\mathbb {T}^3,\) it is, an absolute partially hyperbolic diffeomorphism on \(\mathbb {T}^3\) homotopic to a linear Anosov automorphism of the \(\mathbb {T}^3.\) We can prove that if \(f: \mathbb {T}^3 \rightarrow \mathbb {T}^3 \) is a volume preserving DA diffeomorphism homotopic to a linear Anosov A, such that the center Lyapunov exponent satisfies \(\lambda ^c_f(x) > \lambda ^c_A > 0,\) with x belongs to a positive volume set, then the center foliation of f is non absolutely continuous. We construct a new open class U of non Anosov and volume preserving DA diffeomorphisms, satisfying the property \(\lambda ^c_f(x) > \lambda ^c_A > 0\) for \(m-\)almost everywhere \(x \in \mathbb {T}^3.\) Particularly for every \(f \in U,\) the center foliation of f is non absolutely continuous. |
| Databáze: | OpenAIRE |
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