Year: 2026
Type: preprint
Abstract: We study the statistical properties of partially hyperbolic diffeomorphisms with a two-dimensional center exhibiting mixed behavior, without assuming a dominated splitting inside the center. We introduce the notion of an expanding on average for partially hyperbolic diffeomorphism and, under a center jacobian assumption, we prove the existence of finitely many ergodic hyperbolic SRB measures, and show the strong positive recurrence property, which implies that each SRB measure, up to a period, satisfies exponential decay of correlations, among other strong statistical laws. We apply our results to several examples.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Fundação de Amparo à Pesquisa do Estado de Minas Gerais, Agencia Nacional de Investigación y Desarrollo
Awards: G1207375514, G1426168670, LYAPUNOV EXPONENTS OF PARTIALLY HYPERBOLIC DIFFEOMORPHISMS, Ergodic Theory for Weakly Hyperbolic Dynamical Systems, SEP Collaborative: Alkaliphilic microalgae-based sustainable & scalable processes for renewable fuels and products, G7494281705, G7788968503, SKEW PRODUCTS FORTEMENTE DISSIPATIVOS
OpenAlex ID: W7223000435