This paper surveys applications of low-dimensional topology to the study of the dynamics of
iterated homeomorphisms on surfaces. A unifying theme in the paper is the analysis and …

Many systems exhibit behaviour which can be described by three coupled oscillators.
Provided the coupling is not too strong, such systems can be modelled by maps of the two …

This paper studies homeomorphisms of surfaces isotopic to the identity by means of purely
topological methods and Brouwer theory. The main development is a novel theory of orbit …

Beginning with Sir Isaac Newton, Differential Equations have many applications in natural
science and engineering. Mainly, mathematical models of this applications lead to nonlinear …

We give an equivalent condition for the existence of a semi-conjugacy to an irrational
rotation for conservative homeomorphisms of the two-torus. This leads to an analogue of …

Abstract top For a dynamical system (X, f) and a function φ: X→ ℝ N the rotation set is
defined. The case when (X, f) is a transitive subshift of finite type and φ depends on the …

This article deals with nonwandering (eg area-preserving) homeomorphisms of the torus
T^2 which are homotopic to the identity and strictly toral, in the sense that they exhibit …

We study the rotation sets for homeomorphisms homotopic to the identity on the torus,. In the
conservative setting, we prove that there exists a Baire residual subset of the set of …

The main theme of this paper is to estimate, for self-maps f: X→ X of compact polyhedra, the
asymptotic Nielsen number N∞(f) which is defined to be the growth rate of the sequence {N …

Every convex polygon with rational vertices is a rotation set Page 1 Ergod Th & Dynam Sys (1992),
12, 333-339 Printed in Great Britain Every convex polygon with rational vertices is a rotation …