### 17/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Cristodor Ionescu, *Institute of Mathematics, Romanian Academy, Bucharest*

### Some remarks on evolutions

We present some result concerning evolutions of Noetherian local
rings of characteristic zero using Andre-Quillen homology of
commutative rings.

### 12/06/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building

Christopher Earles, *Rice University, Houston*

### Residue Theorems and Lie Algebroid Invariants

The recent work of Harvey and Lawson has resulted in a family of
residue theorems relating the singular sets (viewed as rectifiable
currents) of a vector bundle map to the Chern-Weil characteristic
forms of the bundles. Many of the classical singularity theorems
(e.g., the Argument Principle, the Poincare-Hopf Index Theorem, and
the Riemann-Roch Theorem) are special cases of these more general
formulae.
In this talk, I will review briefly the techniques used by
Harvey and Lawson and give an account of current work to extend
these to the study of Lie algebroids.

### 03/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Renato Iturriaga, *CIMAT, Guanajuato*

### Convergence of viscosity solutions of random Hamilton Jacobi
equations

### 27/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Miguel Rodríguez Olmos, *Instituto Superior Técnico*

### The topology of symplectic quotients for cotangent bundles

### 20/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Claudia Valls, *Università di Roma*

### Weak KAM Theory for multidimensional maps

### 13/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

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

### Ergodic semifocusing billiards

### 06/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Rui Loja Fernandes, *Instituto Superior Técnico*

### Linearization of Poisson Brackets

### 29/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Luis Barreira, *Instituto Superior Técnico*

### Poincaré recurrence, geodesic flows, hyperbolic geometry

Today, we are arguably in possession of a satisfactory approach to
a quantitative description of recurrence. *As one knows well:
Poincaré only established that orbits return infinitely
often, not how often or when they return.*
This will be a colloquium type exposition of recent results that
shed new light on the subject, also discussing joint work with
Benoît Saussol, Christian Wolf, and Gianluigi Del Magno. The
talk will include the view of the (maybe classical) hyperbolic
geometer and briefly some consequences for number theory. No
prerequisites from dynamical systems or ergodic theory will be
necessary.

### 08/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Tanya Schmah, *University of Warwick*

### The local geometry of symmetric Hamiltonian systems on cotangent
bundles

### 01/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jonathan Wattis, *University of Nottingham*

### A Coarse-graining approximation for the Becker-Doring equations

### 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*

### On the dimension and smoothness of attractors

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

Alexei Davydov, *Vladimir State University, Russia*

### 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.

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

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

### 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.

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

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

### 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.

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

Jan Chabrowski, *The University of Queensland*

### The Neumann Problem with Critical Sobolev Exponent

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

Philippe Didier, *Université Paris-Sud, Orsay*

### Partial hyperbolicity, accessibility and stable ergodicity

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

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

### Continuity of attractors varying the domain

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

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

### Multifractal analysis of recurrence for smooth dynamical systems

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

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

### 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.