Variational Principles For BS Dimension of Subsets
Chenwei Wang, Ercai Chen
TL;DR
This paper introduces a new definition of BS-dimension using packing methods, establishes its properties, and extends variational principles of entropy to this new dimension, linking it to BS-density measures.
Contribution
It redefines BS-dimension via packing, confirms its properties align with cover-based definitions, and extends entropy variational principles to this new framework.
Findings
BS-dimension defined via packing matches cover-based properties
Bowen's equation holds for the new BS-dimension
Extended variational principles relate BS-dimension to entropy
Abstract
We redefine BS-dimension for Caratheodory structure by packing method. We have the same dimension properties with respect to the cover method and check the Bowen's equation for the new dimension as well. Besides, we consider the relation between the new BS-dimension and upper and lower BS-density respectively. We extend the variational principles of entropy to BS dimension.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Topological and Geometric Data Analysis