Work

Conditioned stochastic stability of equilibrium states on uniformly expanding repellers

Year: 2026

Type: article

Abstract: We propose a notion of conditioned stochastic stability of invariant measures on repellers: we consider whether quasi-ergodic measures of absorbing Markov processes, generated by random perturbations of the deterministic dynamics and conditioned upon survival in a neighbourhood of a repeller, converge to an invariant measure in the zero-noise limit. Under suitable choices of the random perturbation, we find that equilibrium states on uniformly expanding repellers are conditioned stochastically stable. In the process, we contribute to the rigorous foundation for the existence of ‘natural measures’, which were proposed by Kantz and Grassberger [Repellers, semi-attractors, and long-lived chaotic transients. Phys. D , vol. 17(1), 1985, pp. 75–86] to aid the understanding of chaotic transients.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2026.10334

Authors: BERNAT BASSOLS CORNUDELLA, MATHEUS M. CASTRO, JEROEN S. W. LAMB

Institutions: Imperial College London, Universidade Estadual de Campinas (UNICAMP), UNSW Sydney, The University of Tokyo

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550