Seminars on Nonlinear Dynamics of Natural Systems

Similar to the Dynamics of Patterns Days we plan to regularly have (half)day mini-seminars on nonlinear dynamical systems, organized by and for the NDNS+ cluster but open to everyone interested. The first of these will be take place on Friday 7 April 2006, at the Vrije Univer sity in Amsterdam, room F153 of the Math (FEW) Building, De Boelelaan 1081 in walking distance from trainstation Amsterdam Zuid/WTC.

(Directions, see http://www.math.vu.nl/en/contact.php.)

Everybody is cordially invited.

Program

12:30-13:15 Bill Kalies (Florida Atlantic University), Computational dynamics via combinatorial approximation and the Conley index.

13:30-14:15 Hil Meijer (University of Utrecht), CL_Matcont for maps: normal form analysis and branch-switching.

14:30-15:15 Konstantinos Efstathiou (University of Groningen) Hamilton ian monodromy in physical systems.

Abstract for Bill Kalies

In this talk, we will give an overview of a combinatorial framework for developing algorithms in computational dynamics including computer-assisted proofs. We will review some recent work on methods to compute Morse decompositions, Lyapunov functions, and Conley indices. We will show some applications to maps and flows, including fast-slow systems and Leslie models of population dynamics.

Abstract for Hil Meijer

We discuss a new continuation environment for discrete-time dynamical systems: “CL_Matcont”. It is a Matlab Toolbox and is based on CONTENT. It facilitates continuation of codimension one bifurcation curves with respect to two paramters. Along such curves extra degeneracies, codimension 2 bifurcations, occur in generic 2-parameter families. Two new aspects of the toolbox are the automated normal form analysis of such codim-2 bifurcations and branch switching to local codimension one bifurcations rooted at codim 2 points. These aspects are discussed in more detail.

Abstract for Konstantinos Efstathiou

Hamiltonian monodromy is the main obstruction to the existence of global action variables in integrable Hamiltonian systems. We give an overview of the related theory and then we describe how monodromy manifests itself in concrete physical systems. In particular we show what are the implications of monodromy for the joint spectrum of the quantization of an integrable Hamiltonian system. Finally, we discuss fractional monodromy which is a recent generalization of monodromy.

Seminar organizers are

Heinz Hanßmann and Rob Vandervorst