We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts “like an automorphism” on one particular orbit), is itself an automorphism. Then, we consider elements of a different nature, defined by means of homological prope...

In this paper we give sufficient conditions for weak isomorphism of Lebesgue measure-preserving expanding endomorphisms of S1.

We present the theory of hyperbolic dynamics of endomorphisms in. Topics covered are hyperbolic sets, stable manifolds, local product structure , shadowing, spectral decomposition and ^-stability. 0. Introduction In this paper we study a smooth mapping f of a manifold M as a dynamical system. We will discuss both semilocal and global dynamical properties of f, but always under some hyperbolicit...