All, most, some differentiable dynamical systems
- Autores: Michael Shub
- Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé
, Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 99-120 - Idioma: inglés
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Resumen
In the first part of this paper we study dynamical systems from the point of view of algebraic topology. What features of all dynamical systems are reflected by their actions on the homology of the phase space? In the second part we study recent progress on the conjecture that most partially hyperbolic dynamical systems which preserve a smooth invariant measure are ergodic, and we survey the known examples. Then we speculate on ways these results may be extended to the statistical study of more general dynamical systems. Finally, in the third part, we study two special classes of dynamical systems, the structurally stable and the affine. In the first case we study the relation of structural stability to entropy, and in the second we study stable ergodicity in the homogeneous space context.
