Let be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that admits a -invariant dense open set on which it is conjugate to a translation and we study the action of on the compactly connected components of the closed and without interior set .
A field of three-component unit vectors on the dimensional spacetime is considered. Two field configurations with different values of the topological charge cannot be connected by the path of field configurations with a finite Euclidean action. Therefore there is no transition between them. The initial and final configurations are assumed to be continuous at infinity. The asymptotic behaviour of intermediate configurations may be arbitrary. The proof is based on the properties of the degree of...
The aim of this paper is twofold. First we give a characterization of the set of kneading invariants for the class of Lorenz–like maps considered as a map of the circle of degree one with one discontinuity. In a second step we will consider the subclass of the Lorenz– like maps generated by the class of Lorenz maps in the interval. For this class of maps we give a characterization of the set of renormalizable maps with rotation interval degenerate to a rational number, that is, of phase–locking...
We extend the recent results from the class of continuous maps of the interval to the class of continuous maps of the circle. Among others, we give a characterization of -limit sets and give a characterization of sets of transitive points for these maps.
The uniqueness theorem for the ergodic maximal operator is proved in the continous case.
It is shown that if two functions share the same uncentered (two-sided) ergodic maximal function, then they are equal almost everywhere.
Unlike in the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under the transitivity assumption, that an Anosov endomorphism of a closed manifold M is either special (that is, every x ∈ M has only one unstable direction), or for a typical point in M there are infinitely many unstable directions. Another result is the semi-rigidity of the unstable Lyapunov exponent of a codimension one Anosov endomorphism that is C¹-close to a linear endomorphism...