The variation of invariant graphs in forced systems - Sorbonne Université
Article Dans Une Revue Chaos: An Interdisciplinary Journal of Nonlinear Science Année : 2018

The variation of invariant graphs in forced systems

Anthony Quas
  • Fonction : Auteur

Résumé

In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature , sync function Lipschitz continuity and differentiability have been proved to hold depending on the derivative of the base reciprocal, if not on its Lyapunov exponent. However, forcing topological features can also impact the sync function regularity. Here, we estimate the total variation of sync functions generated by one-dimensional Markov maps. A sharp condition for bounded variation is obtained depending on parameters, which involves the Markov map topological entropy. The results are illustrated with examples.
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Dates et versions

hal-01879947 , version 1 (24-09-2018)

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Bastien Fernandez, Anthony Quas. The variation of invariant graphs in forced systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018, 28 (8), pp.083101. ⟨10.1063/1.5026551⟩. ⟨hal-01879947⟩
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