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ВИДЕОТЕКА |
Конференция «Hyperbolic Dynamics and Structural Stability», посвященная 85-летию Д. В. Аносова
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Local rigidity of abelian actions of parabolic toral automorphisms with (at least) one step-2 generator B. R. Fayad Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris |
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Аннотация: Two famous manifestations of local rigidity are KAM rigidity of Diophantine torus translations and smooth rigidity of hyperbolic or partially hyperbolic higher rank actions. Damjanovic and Katok proved local rigidity for partially hyperbolic higher rank affine actions on tori. To complete the study of local rigidity of affine We say that a linear map We say that a We say that an affine If \begin{equation}\label{eq_Commut} (a+f)\circ (b+g)=(b+g)\circ (a+f), \end{equation} $$ \|f\|_r\leq \varepsilon, \quad \|g\|_r\leq \varepsilon, \quad \widehat f:= \int_{\mathbb T^d} f d\lambda=0, \quad \widehat g:=\int_{\mathbb T^d} g d\lambda=0, $$ then there exists $H=\mathrm{Id} +h \in \text{Diff}^\infty_\mu (\mathbb T^d)$ such that \begin{equation}\label{eq_System} H \circ (a+f) \circ H^{-1} = a, \quad H \circ (b+g) \circ H^{-1} = b. \end{equation} We denote by $$\mathcal T(A,B):=\{\alpha, \beta\in \mathbb R^d : (A-\mathrm{Id})\beta=(B-\mathrm{Id})\alpha\}.$$ Theorem. Given a commuting pair
This is a joint work with Danijela Damjanovic and Maria Saprykina. Язык доклада: английский |