arXiv subjects

Vahatra Rabodonandrianandraina

Publications and source records attributed to Vahatra Rabodonandrianandraina.

2 recordsLinked to original sources

arXiv2021

Critical intermittency in rational maps

Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in iterated function systems, and involves a superattracting periodic orbit. This paper will provide and study examples of iterated function systems by two rational maps on the Riemann sphere that give rise to critical intermittency. The main ingredient for this is a superattracting fixed point for one map that is mapped onto a common repelling fixed point by the other map. We include a study of topological properties such as topological transitivity.

math.DS↗

arXiv2018

On-off intermittency and chaotic walks

We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or positive fiber Lyapunov exponent at the other endpoint. We prove the appearance of on-off intermittency. This is done using the equivalent description of chaotic walks: random walks driven by the doubling map. The analysis further relies on approximating the chaotic walks by Markov random walks, that are constructed using Markov partitions for the doubling map.

math.DS↗