Generating Simplicial Complexes
Daniel J. Pons, Pierre P. Romagnoli
TL;DR
This paper introduces new complexity functions for dynamical systems acting on simplicial complexes, revealing notable properties especially in expansive systems, and revisits known examples while presenting new ones.
Contribution
It develops novel complexity measures for group and semigroup actions on simplicial complexes, expanding understanding of their dynamical behaviors.
Findings
Remarkable properties observed in expansive systems
Revisiting known examples with new insights
Presentation of new examples of dynamical systems
Abstract
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For expansive systems remarkable properties are observed. Known examples are revisited and new examples are presented.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Geometric and Algebraic Topology