A triple boundary lemma for surface homeomorphisms

The Rokhlin lemma for homeomorphisms of a Cantor set

For a Cantor set X, let Homeo(X) denote the group of all homeo-morphisms of X. The main result of this note is the following theorem. Several corollaries of this result are given. In particular, it is proved that for any aperiodic T ∈ Homeo(X) the set of all homeomorphisms conjugate to T is dense in the set of aperiodic homeomorphisms. 0. Introduction. One of the most useful results in ergodic ...

Simple Braids for Surface Homeomorphisms

Let S be a compact, oriented surface with negative Euler characteristic and let f : S → S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (~ p, q), then there exists a simple braid with the same rotation vector.

Recurrent Surface Homeomorphisms

An orientation-preserving recurrent homeomorphism of the twosphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

A Boundary Point Lemma for Black-scholes Type Operators

We prove a sharp version of the Hopf boundary point lemma for Black-Scholes type equations. We also investigate the existence and the regularity of the spatial derivative of the solutions at the spatial boundary.