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Distribution of Typical Orbits for a Skew-product Map Generated by Random Dynamics of Finitely Many Rational Maps by Sridharan, Shrihari; Tikekar, Sharvari Neetin; Tiwari, Atma Ram is a scholarly article available to read on EtoBox.

What is Distribution of Typical Orbits for a Skew-product Map Generated by Random Dynamics of Finitely Many Rational Maps about?

In this paper, we consider the dynamics of a skew-product map defined on the Cartesian product of the symbolic one-sided shift space on $N$ symbols and the complex sphere where we allow $N$ rational maps, $R_{1}, R_{2}, \cdots, R_{N}$, each with degree $d_{i};\ 1 \le i \le N$ and with at least one $R_{i}$ in the collection whose degree is at least $2$. We obtain results regarding the distribution of pre-images of points and the periodic points in a subset of the product space (where the skew-product map does not behave normally). We further explore the ergodicity of the Sumi-Urbanskii (equilibrium) measure associated to some real-valued H\"{o}lder continuous function defined on the Julia set of the skew-product map and obtain estimates on the mean deviation of the behaviour of typical orbits, violating such ergodic necessities.

Author

Sridharan, Shrihari; Tikekar, Sharvari Neetin; Tiwari, Atma Ram

Published

2019

Language

EN