In the case of a two degrees of freedom system the fibers of Tf on the orbit space are the
trajectories of the reduced system. The critical Tf fibers, which might be points, respectively …

Universitext Page 1 123 Universitext Qualitative Theory of Planar Differential Systems Freddy
Dumortier Jaume Llibre Joan C. Artés Page 2 Page 3 123 Freddy Dumortier, Jaume Llibre …

Pattern formation in physical systems is one of the major research frontiers of mathematics.
A central theme of this book is that many instances of pattern formation can be understood …

In this paper we survey the topic of time-reversal symmetry in dynamical systems. We begin
with a brief discussion of the position of time-reversal symmetry in physics. After defining …

Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

The biologist JBS Haldane, when asked what we can learn about the Creator by examining
the world, is said to have replied “an inordinate fondness for beetles”[705]. Today's …

Page 1 Number 421 HW Broer GB Huitema F. Takens and BLJ Braaksma Unfoldings and
bifurcations of quasi-periodic tori Q Memoirs of the American Mathematical Society Providence …

I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

Some theorems by LP Sil'nikov, which describe the dynamics in the neighbourhood of
homoclinic orbits, bi-asymptotic to a saddle-focus, and initially proved for real analytic vector …

This paper first summarizes the theory of quasi-periodic bifurcations for dissipative
dynamical systems. Then it presents algorithms for the computation and continuation of …