Inverse pressure for finitely generated semigroups. (September 2022)

• Record Type: Journal Article
• Authors: Biś, Andrzej; Mihailescu, Eugen
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: primary 37B05, 37A15, 37A35, 37C45, 37D20; Dynamics of endomorphisms -- Inverse pressure -- Semigroups of maps -- Hausdorff dimension -- Stable/unstable cone fields for smooth maps -- Local entropy; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112942
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We introduce and study an inverse topological pressure P − and its capacities for multi-potentials with respect to the dynamics of finitely generated semigroups G of non-invertible maps (see Mihailescu, 2021) on arbitrary sets Y in compact metric spaces X . These notions are very different from the (forward) pressure notions studied previously and reflect other aspects of the semigroup dynamics. We prove several properties of this inverse pressure. Examples of inverse entropy/pressure for semigroups are also discussed. Then, we consider a G -invariant compact set Λ for a semigroup G of smooth endomorphisms on a manifold M, having a G -stable cone field and a G -unstable cone field over Λ . The inverse pressure of the stable multi-potential is applied to obtain dimension estimates for slices through Λ which are transversal to the unstable directions.