We study invariant measures and thermodynamic formalism for a class of endomorphisms FT which are only piecewise differentiable on countably many pieces non-conformal. The endomorphism has random generated limit sets JT,ω in stable fibers. prove Global Volume Lemma implying that the projections equilibrium exact dimensional non-compact global basic set JT. A dimension formula these is obtained ...

Abstract We consider continuous free semigroup actions generated by a family $(g_y)_{y \,\in \, Y}$ of endomorphisms compact metric space $(X,d)$ , subject to random walk $\mathbb P_\nu =\nu ^{\mathbb N}$ defined on shift $Y^{\mathbb where $(Y, d_Y)$ is with finite upper box dimension and $\nu $ Borel probability measure Y . With the aim elucidating impact mean dimension, we prove variational p...

We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...

We give conditions for the exactness of Rokhlin skew products, apply these to random walks on locally compact, second countable topological groups and obtain that the Poisson boundary of a globally supported random walk on such a group is weakly mixing. S is a measurable homomorphism). We give (theorem 2.3) conditions for the exactness of the Rokhlin endomorphism T = These conditions are applie...

We give conditions for the exactness of Rokhlin skew products, apply these to random walks on locally compact, second countable topological groups and obtain that the Poisson boundary of a globally supported random walk on such a group is weakly mixing. We give (theorem 2.3) conditions for the exactness of the Rokhlin endomorphism T = These conditions are applied to random walk-endomorphisms. M...

Endomorphisms of stable planes are introduced, and it is shown that these are injective, locally constant or collapsed. Examples are studied, and it is shown that there are stable planes admitting \substantially more" endomorphisms than automorphisms. It seems to be a rather popular feeling that geometry is the domain of groups and symmetry, whereas asymmetry and semigroups have been banished t...

We give conditions for the exactness of Rokhlin skew products, apply these to random walks on locally compact, second countable topological groups and obtain that the Poisson boundary of a globally supported random walk on such a group is weakly mixing. We give (theorem 2.3) conditions for the exactness of the Rokhlin endomorphism T = These conditions are applied to random walk-endomorphisms. M...

We study relations between the quadraticity of Kuranishi family a coherent sheaf on complex projective scheme and formality DG-Lie algebra its derived endomorphisms. In particular, we prove that for polystable smooth surface endomorphisms is formal if only quadratic.

We extend the notion of ‘homomorphism-homogeneity’ to a wider class of kinds of maps than previously studied, and we investigate the relations between the resulting notions of homomorphism-homogeneity, giving several examples. We also give further details on related work reported in [Deborah Lockett and John K. Truss, Generic endomorphisms of homogeneous Structures,in ‘Groups and model theory’,...

Abstract. We present a systematic way to generate critically finite endomorphisms of Pn. These maps arise in the context of Teichmüller theory, specifically in Thurston’s topological characterization of rational maps. The dynamical objects for the endomorphisms correspond to central objects from Thurston’s theorem. Our theorems build infinitely many of these endomorphisms; in fact, a large numb...