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arXiv · 2405.07661

A note on the topological synchronisation of unimodal maps

Michele Gianfelice
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Abstract

In this note we complete the analysis carried on in \cite{CGSV} about the topological synchronisation of unimodal maps of the interval coupled in a master-slave configuration, by answering to the questions raised in that paper. Namely, we compute the weak limits of the invariant measure of the coupled system as the coupling strength $k\in\left( 0,1\right) $ tends to $0$ and to $1$ and discuss the uniqueness of the invariant measure of its random dynamical system counterpart, proving that the convergence of the associated Markov chain to its unique stationary measure is geometric. [CGSV] Caby Th., Gianfelice M., Saussol B., Vaienti S. "Topological synchronisation or a simple attractor?" Nonlinearity Vol. 36, no. 7, pp. 3603-3621 (2023).

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Michele Gianfelice. 2024-11-28. A note on the topological synchronisation of unimodal maps. https://arxiv.org/abs/2405.07661

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