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 …

Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

This article is a methodological manual for those who are interested in chaotic dynamics. An
exposition is given on the foundations of the theory of deterministic chaos that originates in …

Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have
the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled …

В течение долгого времени представление о хаосе ассоциировалось с допущением,
что в системе необходимо, по крайней мере, возбуждение чрезвычайно большого …

The paper also contains estimates on the amount of surviving tori. The worst situation
happens when the initial tori are normally elliptic. In this case, a torus (identified by the …

In this paper, we present and illustrate a general methodology to apply KAM theory in
particular problems, based on an a posteriori approach. We focus on the existence of real …

We consider perturbations of integrable, area preserving nontwist maps of the annulus
(those are maps in which the twist condition changes sign). These maps appear in a variety …

MHD equilibria with nonconstant pressure in nondegenerate toroidal domains Page 1 © 2023
European Mathematical Society Published by EMS Press J. Eur. Math. Soc. (Online first) DOI …

We study the accumulation of an invariant quasi-periodic torus of a Hamiltonian flow by
other quasi-periodic invariant tori. We show that an analytic invariant torus T 0 with …