Recurrent Solutions and Mean Exponential Dichotomy for Dynamic Equations on Time Scales

• Mai Yang ^[1] ; Yongguang Yu ^[1] ; Jiahui Feng ^[1]
  1. [1] Beijing Jiaotong University

     Beijing Jiaotong University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 6, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • As a particular class of hybrid dynamical systems, dynamic equations on time scales provide an accessible framework to describe discrete and continuous dynamics in a unified manner. Different from uniform and nonuniform hyperbolicities, mean hyperbolicity emphasizes non-hyperbolic behavior and fixed average contraction and expansion rates during the evolution process. With respect to dynamic equations on time scales, we provide the sufficient conditions for mean exponential dichotomy, where generalized exponential function and growth condition at right-scattered points are key techniques. Moreover, the existence of recurrent solutions based on mean exponential dichotomy are shown, including rotating periodic, almost periodic, almost automorphic, and asymptotically almost automorphic solutions on time scales. Particularly, the roughness of mean exponential dichotomy can be applied to the stability theory of dynamic models on time scales.

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