Numerical Treatment of Dynamical Systems

last update: March 7th, 2002

Dobbiaco (Bolzano - Italy), June 17-21, 2002

The Dipartimento di Scienze Matematiche of the University of Trieste is organizing a Summer School on 'Numerical Treatment of Dynamical Systems'  in Dobbiaco (Bolzano - Italy) in the period June 17-21, 2002. The school is partially supported by the 'Istituto Nazionale di Alta Matematica' - Gruppo Nazionale di Calcolo Scientifico.

In line with the previous editions, the aim of the School is to introduce young researches to prominent topics of recent development in Numerical Analysis.

The participants are assumed to have a basic knowledge of numerical methods for ordinary differential equations.


The School consists of invited lectures. The invited speakers are:

    Luca Dieci, School of Mathematics, Georgia Institute of Technology, USA

   Tony R. Humphries, School of Mathematical Sciences, University of Sussex, UK


The title of the lectures is the following:

June 17
June 18
June 19
June 20
June 21
    Humphries - 1
    Dieci - 2
    Dieci - 4
    Dieci - 5
    Humphries - 6
coffee break coffee break coffee break coffee break  coffe break
    Dieci - 1
    Humphries - 3
    Humphries - 4
    Humphries - 5
lunch lunch lunch lunch  lunch
    Humphries - 2
    Dieci - 3
    EXCURSION  14.30-16.00 
    Dieci - 6

Humphries - 1: Introduction. Maps and flows. Examples of continuous and discrete dynamical systems.
                         Invariant sets. Attractors.
Dieci - 1: Introduction. ODEs: smoothness with respect to initial conditions and parameters.
                Invariant manifolds. Stable/unstable manifolds of equilibria: the graph transform.
Humphries - 2: Numerical methods as dynamical systems. Existence, uniqueness, smoothness.
                         Upper semi-continuity of attractors.
Dieci - 2: Equilibria, path following and bifurcations.
Humphries - 3: Spurious solutions and stability.
Dieci - 3: Periodic orbits, computation and continuation. Bifurcations and computation of Floquet multipliers.
Dieci - 4:  Connecting orbits between equilibria and between periodic orbits.
Humphries - 4: Approximation of local stable/unstable manifolds. Lower semi-continuity of attractors.
Dieci - 5: Globalization of stable/unstable manifolds.
Humphries - 5: Hamiltonian systems.
Dieci - 6: Computation of invariant tori. Lyapunov exponents.
Humphries - 6: Adaptive time-stepping methods.
Dieci/Humphries: Question session and discussion of research topics, open problems, perspectives.

Please, note:

        For reservations you must directly contact the Hotel saying the title 'Convegno Matematica Trieste' and you must say the dates of arrival/departure (Apparthotel Germania, ph. +39 0474 972160, fax +39 0474 973272).

Please, send your registration form by April 30, 2002 to (Torelli Lucio - Dipartimento di Scienze Matematiche - Università degli Studi di Trieste - 040 558-2677 - fax 040 558-2636)


Summer School on Numerical Methods for ODEs (Dobbiaco (BZ) 3-7 luglio 2000)

Summer School on Time Delay Equations and Control Theory (Dobbiaco (BZ) June, 25-29 2001)

For any information

                    Lucio TORELLI                        Marino ZENNARO

                    Alfredo BELLEN