Statistical Stability for Equilibrium States

Freitas, Jorge Milhazes; Todd, Michael J.

doi:10.1007/978-3-642-14788-3_24

Cited by 1 publication

(1 citation statement)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Corollary 1.2 concerns the topological stability for M α when varying α. A related area of study for Manneville-Pomeau maps is the measure theoretical statistical stability, where the behaviour of the absolutely continuous invariant measure for M α is studied when varying α, see for example the recent works by Freitas and Todd [11] and Baladi and Todd [3].…”

Section: Under These Assumptions If For Anymentioning

confidence: 99%

Stability and perturbations of countable Markov maps

2018

View full text Add to dashboard Cite

We study the pointwise perturbations of countable Markov maps with infinitely many inverse branches and establish the following continuity theorem: Let T k and T be expanding countable Markov maps such that the inverse branches of T k converge pointwise to the inverse branches of T as k → ∞. Then under suitable regularity assumptions on the maps T k and T the following limit exists:where θ k is the topological conjugacy between T k and T and dim H stands for the Hausdorff dimension. This is in contrast with the fact that other natural quantities measuring the singularity of θ k fail to be continuous in this manner under pointwise convergence such as the Hölder exponent of θ k or the Hausdorff dimension dim H (µ•θ k ) for the preimage of the absolutely continuous invariant measure µ for T . As an application we obtain a perturbation theorem in non-uniformly hyperbolic dynamics for conjugacies between intermittent Manneville-Pomeau maps x → x + x 1+α mod 1 when varying the parameter α.

show abstract

Section: Under These Assumptions If For Anymentioning

confidence: 99%