Showing papers by "David Ruelle published in 1975"
TL;DR: In this article, the Whitney sum of three (Tf t )-invariant continuous subbundles of a Riemann manifold is used to define hyperbolic tangent bundles.
Abstract: Let M be a compact (Riemann) manifold and (f t ): M → M a differentiable flow A closed (f t )-invariant set ∧ ⊂ M containing no fixed points is hyperbolic if the tangent bundle restricted to ∧ can be written as the Whitney sum of three (Tf t )-invariant continuous subbundles
$${T_\Lambda }M = E + {E^s} + {E^u}$$
where E is the one-dimensional bundle tangent to the flow, and there are constants c λ>0 so that
$$(a)||T{f^t}(v)||\underset{\raise03em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } c{e^{ - \lambda t}}||v||forv \in {E^s},t\underset{\raise03em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } 0and$$
$$(b)||T{f^{ - 1}}(v)||\underset{\raise03em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } c{e^{ - \lambda t}}||v||forv \in {E^u},t\underset{\raise03em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } 0$$
727 citations
571 citations
TL;DR: In this article, the authors describe a geometrical object in a manifold which determines by integration of differential forms a closed current in the sense of de Rham, which is made up of a partial foliation in the manifold which is oriented and provided with a transversal measure.
200 citations
01 Jan 1975
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/conditions) are defined, i.e., toute utilisation commerciale ou impression systématique is constitutive of an infraction pénale.
Abstract: © Société mathématique de France, 1976, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
12 citations