اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPerturbation de la dynamique de diffeomorphismes en topologie C^1 / Perturbation of the dynamics of diffeomorphisms in the C^1-topology
98
0
0.0
(
0
)
تأليف
Sylvain Crovisier
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Les travaux presentes dans ce memoire portent sur la dynamique de diffeomorphismes de varietes compactes. Pour letude des proprietes generiques ou pour la construction dexemples, il est souvent utile de savoir perturber un syst`eme. Ceci soul`eve generalement des probl`emes delicats : une modification locale de la dynamique peut engendrer un changement brutal du comportement des orbites. En topologie C^1, nous proposons diverses techniques permettant de perturber tout en contr^olant la dynamique : mise en transversalite, connexion dorbites, perturbation de la dynamique tangente, realisation dextensions... Nous en tirons diverses applications `a la description de la dynamique des diffeomorphismes C^1-generiques. <p> This memoir deals with the dynamics of diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamic may cause a radical change in the behavior of the orbits. For the C^1 topology, we propose various techniques which allow to perturb while controlling the dynamic: setting in transversal position, connection of orbits, perturbation of the tangent dynamics,... We derive various applications to the description of the C^1-generic diffeomorphisms.
قيم البحث
اقرأ أيضاً
We study the ergodic theory of non-conservative C^1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose supports coincide with the homoclinic class. Second, we show that generic
(for the weak topology) ergodic measures of C^1-generic diffeomorphisms are nonuniformly hyperbolic: they exhibit no zero Lyapunov exponents. Third, we extend a theorem by Sigmund on hyperbolic basic sets: every isolated transitive set L of any C^1-generic diffeomorphism f exhibits many ergodic hyperbolic measures whose supports coincide with the whole set L. In addition, confirming a claim made by R. Mane in 1982, we show that hyperbolic measures whose Oseledets splittings are dominated satisfy Pesins Stable Manifold Theorem, even if the diffeomorphism is only C^1.
Denote by $DC(M)_0$ the identity component of the group of the compactly supported $C^r$ diffeomorphisms of a connected $C^infty$ manifold $M$. We show that if $dim(M)geq2$ and $r eq dim(M)+1$, then any homomorphism from $DC(M)_0$ to ${Diff}^1(R)$ or ${Diff}^1(S^1)$ is trivial.
Metric entropies along a hierarchy of unstable foliations are investigated for $C^1$ diffeomorphisms with dominated splitting. The analogues of Ruelles inequality and Pesins formula, which relate the metric entropy and Lyapunov exponents in each hierarchy, are given.
We correct an error that occurs with certain frequency in popular literature of Special Relativity, namely that supposedly that mass of moving objects depends on the relative velocity of the object and the observer. In this pedagogical paper, we expl
ain that it is more correct to state that the linear momentum and the kinetic energy increase with velocity, while the mass is in fact an invariant, independent of the motion of the object and of the observer. We give a few paradoxes that arise if one assumes a mass-dependent velocity.
In the Nineties, Michel Herman conjectured the existence of a positive measure set of invariant tori at an elliptic diophatine critical point of a hamiltonian function. I construct a formalism for the UV-cutoff and prove a generalised KAM theorem which solves positively the Herman conjecture.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
