Work

A simple example of pathological foliations in skew-product diffeomorphisms

Year: 2024

Type: article

Abstract: Inspired by examples of Katok and Milnor [3], we construct simple examples of skew-product volume preserving diffeomorphisms where the center foliation is pathological in the sense that there is a full measure set whose intersection with any center leaf contains at most one point. Comparing with other examples in literature, our mechanism for producing such pathological foliation is simple and elementary.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2024147

Authors: Zhihong Xia, Peizheng Yu

Institution: Shandong University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404660286

FWCI:

Cites: 6

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Related to: 10