THE VARIATIONAL PRINCIPLE FOR A BS DIMENSION OF SUBSETS FOR NON-AUTONOMOUS DYNAMICAL SYSTEMS

doi:10.1007/s10473-026-0118-1

Abstract

Abstract: In this manuscript, we consider a non-autonomous dynamical system. Using the Carathéodory structure, we define a BS dimension on an arbitrary subset and obtain a Bowen's equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian [24]. Moreover, we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems. Finally, we also get an analogue of Billingsley's theorem for the BS dimension of non-autonomous dynamical systems.

Key words: non-autonomous dynamical systems, BS dimension, Bowen's equation, variational principle

CLC Number:

37B55

Zhongxuan YANG^*, Xiaojun HUANG. THE VARIATIONAL PRINCIPLE FOR A BS DIMENSION OF SUBSETS FOR NON-AUTONOMOUS DYNAMICAL SYSTEMS[J].Acta mathematica scientia,Series B, 2026, 46(1): 311-329.

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