In this note we complete the analysis carried on in Caby et al (2023 Nonlinearity 36 3603–21) 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 2 (0, 1) 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.
A note on the topological synchronization of unimodal maps
Michele Gianfelice
2025-01-01
Abstract
In this note we complete the analysis carried on in Caby et al (2023 Nonlinearity 36 3603–21) 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 2 (0, 1) 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.File in questo prodotto:
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