Counting functions over periodic orbits of a skew-product map
Subith Gopinathan, Bharath Krishna Seshadri, Shrihari Sridharan
TL;DR
This paper studies counting functions related to periodic orbits in a skew-product map associated with a rational semigroup, providing comparability results for these functions.
Contribution
It introduces new comparability results for counting functions over periodic orbits in skew-product maps linked to rational semigroups.
Findings
Establishes comparability of counting functions
Analyzes properties of ergodic sums along periodic orbits
Connects dynamics of rational semigroups with counting functions
Abstract
In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise, we obtain some comparability results for the above mentioned counting functions.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Operator Algebra Research · Stochastic processes and statistical mechanics