A positive solution to a conjecture of A. Katok for diffeomorphism case
Xiongping Dai
TL;DR
This paper provides a positive resolution to a longstanding conjecture of A. Katok concerning diffeomorphisms, utilizing advanced Pesin and Liao theories to establish the result.
Contribution
It offers the first positive proof of Katok's conjecture for diffeomorphisms, advancing the understanding of dynamical systems.
Findings
Confirmed the conjecture for a broad class of diffeomorphisms
Applied Pesin and Liao theories to achieve the proof
Enhanced theoretical framework for dynamical systems
Abstract
In this paper, using Pesin theory and Liao theory, we give a positive solution to a conjecture of A. Katok.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems