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Analysis, Geometry, and Dynamical Systems Seminar   RSS

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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
, 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
, Instituto Superior Técnico

Linearization of Poisson Brackets

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

A Coarse-graining approximation for the Becker-Doring equations

25/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, 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 R3 . 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
, 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
, 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
, IME, Universidade de São Paulo

Continuity of attractors varying the domain

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

16/01/2003, 17:00 — 18:00 — Room P3.10, Mathematics Building
Jack Hale, Georgia Institute of Technology

Coupled oscillators on a circle

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