Measures of intermediate pressures for geometric Lorenz attractors

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Shi, Yi, Wang, Xiaodong
Format: Preprint
Publié: 2024
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866912067124985856
author Shi, Yi
Wang, Xiaodong
author_facet Shi, Yi
Wang, Xiaodong
contents Pressure measures the complexity of a dynamical system concerning a continuous observation function. A dynamical system is called to admit the intermediate pressure property if for any observation function, the measure theoretical pressures of all ergodic measures form an interval. We prove that the intermediate pressure property holds for $C^r (r\geq 2)$ generic geometric Lorenz attractors while it fails for $C^r (r\geq 2)$ dense geometric Lorenz attractors, which gives a sharp contrast. Similar results hold for $C^1$ singular hyperbolic attractors.
format Preprint
id arxiv_https___arxiv_org_abs_2410_07521
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Measures of intermediate pressures for geometric Lorenz attractors
Shi, Yi
Wang, Xiaodong
Dynamical Systems
Pressure measures the complexity of a dynamical system concerning a continuous observation function. A dynamical system is called to admit the intermediate pressure property if for any observation function, the measure theoretical pressures of all ergodic measures form an interval. We prove that the intermediate pressure property holds for $C^r (r\geq 2)$ generic geometric Lorenz attractors while it fails for $C^r (r\geq 2)$ dense geometric Lorenz attractors, which gives a sharp contrast. Similar results hold for $C^1$ singular hyperbolic attractors.
title Measures of intermediate pressures for geometric Lorenz attractors
topic Dynamical Systems
url https://arxiv.org/abs/2410.07521