From the reviews:" This book is concerned with the application of methods from dynamical
systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a …

Several distinctive aspects make Dynamical Systems unique, including: treating the subject
from a mathematical perspective with the proofs of most of the results includedproviding a …

One-dimensional dynamics has developed in the last decades into a subject in its own right.
Yet, many recent results are inaccessible and have never been brought together. For this …

This article surveys results and conjectures in dynamical systems and other areas that
describe properties of 'almost every'function in some space, using a probabilistic (or …

We present two hypotheses on the mathematical mechanism underlying bursting dynamics
in a class of differential systems:(1) that the transition from continuous firing of spikes to …

We study unimodal interval maps T with negative Schwarzian derivative satisfying the Collet-
Eckmann condition| DT n (Tc)|≧ Kλ cn for some constants K> 0 and λ c> 1 (c is the critical …

We construct the “spectral” decomposition of the sets, ω (f)=∪ ω (x) and Ω (f) for a
continuous map f:[0, 1]→[0, 1]. Several corollaries are obtained; the main ones describe the …

Our aim is to show that the Julia-Fatou--Sullivan structure theory for the dynamics of rational
maps is also valid for smooth endomorphisms of the circle (and of the interval) under …

Many biperiodic flows can be modelled by maps of a circle to itself. For such maps the
transition from zero to positive topological entropy can be achieved in several ways. We …

This paper considers one parameter families of diffeomorphisms {F t} in two dimensions
which have a curve of dissipative saddle periodic points P t, ie F tn (P t)= P t and| det DF tn …