The problem of transition to chaos, i.e. the destruction of invariant circles or KAM (Kolmogorov-Arnold-Moser) curves, in area preserving nontwist maps is studied within the renormalization group framework. Nontwist maps are maps for which the twist condition is violated along a curve known as the shearless curve. In renormalization language this problem is that of nding and studying the xed po...

This paper deals with cocycles over ergodic metric dynamical systems with values in the semi-direct product of Z 2 and R. We show that such cocycles are recurrent under very general assumptions. Furthermore, we give criteria for the existence of invariant measures for group valued cocycles. With that, examples of continuous random dynamical systems on a compact interval without random xed point...

The wedge-entry problem can be formulated as an integral equation , involving a parameter , small corresponding to wedges of semi-vertex angle just less than =2. An existence proof for the wedge-entry problem is given in LP]. Numerics using a similar integral equation were rst published in Dob], and recently checked and extended to smaller in ZF]. This report contains the following. I Numerical...

We establish common fixed point theorems related with families of selfmappings on metric spaces. Our results extend, improve, and unify the results due to Fisher (1977, 1978, 1979, 1981, 1984), Jungck (1988), and Ohta and Nikaido (1994). 2000 Mathematics Subject Classification. 47H10, 54H25.

In this paper, we introduce a new class of set-valued contractions and obtain a xed point theoremfor such mappings in complete metric spaces. Our main result generalizes and improves many well-known xed point theorems in the literature.

Nonstandard methods are used to obtain results about sets formed by simple dense canals in the plane. The …rst main result considers internal regions V that contain no standard points and have the property that st(V ) does not disconnect the plane and are bounded by simple closed curves that have small intersection with st(V ): We show that such sets must be somewhat one-dimensional in the sens...