2025/04/27 by Alexander Arbieto, Arbieto, Alexander, Eric Cabezas +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2504.19312
openalex publication_date 2025/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish the existence and finiteness of equilibrium states for a class of partially hyperbolic endomorphisms. In our first result, we assume that the central direction is simple. In the second result, we consider the case where there exists a dominated splitting along the central direction, which is decomposed into one-dimensional subbundles. This latter result extends the work of C. Alvarez and M. Cantarino \citealvarez2022existence to higher-dimensional central directions. Finally, we demonstrate the finiteness of measures of maximal entropy under the assumption that the central direction is one-dimensional and the integrated Lyapunov exponent is bounded away from zero.