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25/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Waldyr Oliva, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos e Instituto de Sistemas e Robótica*

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On the dimension and smoothness of attractors

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18/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Alexei Davydov, *Vladimir State University, Russia*

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Optimal strategies of time averaged optimization of cyclic motion

We consider dynamic inequalities with locally bounded derivatives
on the circle and optimize the time averaged profit along
admissible motions which are defined for all nonegative time. We
describe the nature of optimal strategies, generic swichings
between them when the problem depends additionally from a one
dimensional parameter, and also the respective singularities of the
averaged profit like a function of the parameter.

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11/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

David Krejcirik, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

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Bound States in Curved Quantum Layers

We consider a nonrelativistic quantum particle constrained
to a curved hard-wall layer of constant width built over
a noncompact surface embedded in
${R}^{3}$.
Under the assumption that the surface curvatures vanish
at infinity, we find sufficient conditions which guarantee
the existence of geometrically induced bound states.

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25/02/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Katrin Gelfert, *Max-Planck-Institut für Physik komplexer Systeme, Dresden*

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Lower bounds of the topological entropy

One major significance of the topological entropy is its strong
relation to other dynamical invariants such as Lyapunov exponents,
topological pressure, fractal dimension, and Hausdorff dimension,
which provides our primary motivation. Almost all previous
investigations of the topological entropy have been concerned with
upper bounds. Exact formulas have been derived under strong
smoothness assumptions only. In this talk we will give lower bounds
of the topological entropy of smooth dynamical systems on
Riemannian manifolds which are sharp in some cases. They are
formulated in terms of the phase space dimension and of the
exponential growth rates of a singular value function of the
tangent map. These rates correspond to the deformation of k-volumes
and can for instance be estimated in terms of Lyapunov exponents.
Examples address Henon maps, linear maps, the geodesic flow on a
(not necessarily compact) Riemannian manifold without conjugate
points, and skew product systems.

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18/02/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jan Chabrowski, *The University of Queensland*

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The Neumann Problem with Critical Sobolev Exponent

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11/02/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Philippe Didier, *Université Paris-Sud, Orsay*

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Partial hyperbolicity, accessibility and stable ergodicity

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04/02/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Antônio Luiz Pereira, *IME, Universidade de São Paulo*

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Continuity of attractors varying the domain

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28/01/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Benoît Saussol, *Université de Picardie Jules Verne, Amiens*

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Multifractal analysis of recurrence for smooth dynamical systems

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21/01/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Enrico Valdinoci, *Università degli Studi di Roma Tor Vergata*

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Elliptic tori, periodic solutions and the three body-problem

We prove, under suitable nonresonance conditions, that Hamiltonian
systems with invariant elliptic tori possess periodic orbits of
longer and longer period which accumulate on such tori. We apply
this result to the spatial planetary three-body problem, obtaining
periodic orbits accumulating on linearly stable invariant tori for
such system. Also, we show that the spatial planetary three-body
problem exhibits periodic orbits of any prescribed frequency,
provided that the masses of the planets are small enough with
respect to the inverse of the period.

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16/01/2003, 17:00 — 18:00 — Room P3.10, Mathematics Building

Jack Hale, *Georgia Institute of Technology*

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Coupled oscillators on a circle

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09/01/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building

Rafael de la Llave, *University of Texas, Austin*

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Rigidity properties of hyperbolic systems preserving conformal structures on the invariant distributions

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17/12/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building

Carlos Rocha, *Instituto Superior Técnico*

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Morse-Smale Flows and Order Preserving Semigroups

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10/12/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building

Rahul Pandharipande, *Princeton University*

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Gromov-Witten theory and integrable systems

###
03/12/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building

James Greenberg, *Office of Naval Research, EUA*

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Congestion on Multilane Highways

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26/11/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building

Maribel Gordon, *Universidade da Madeira*

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Um novo espaço de ultradistribuições

###
19/11/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building

Sandra Hayes, *Technische Universität München*

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Detecting chaos using time series

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12/11/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jaroslav Smítal, *Silesian University, Opava*

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Various kinds of chaos in compact metric spaces: recent results and open problems

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05/11/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building

Gianluigi Del Magno, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

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Hyperbolic billiards

###
31/10/2002, 10:00 — 11:00 — Room P3.10, Mathematics Building

José I. Burgos Gil, *Universitat de Barcelona*

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Arakelov theory of non compact Shimura varieties

In this talk I will give an introduction to Arakelov Geometry, focusing on the particular problems that appear when extending the theory to toroidal compactifications of noncompact Shimura varieties.