The variation of invariant graphs in forced systems - Sorbonne Université Access content directly
Journal Articles Chaos: An Interdisciplinary Journal of Nonlinear Science Year : 2018

The variation of invariant graphs in forced systems

Anthony Quas
  • Function : Author

Abstract

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.
Fichier principal
Vignette du fichier
1.5026551.pdf (581.47 Ko) Télécharger le fichier
Origin : Publication funded by an institution

Dates and versions

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

Licence

Attribution

Identifiers

Cite

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⟩
79 View
133 Download

Altmetric

Share

Gmail Facebook X LinkedIn More