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Creators/Authors contains: "Saprykina, Maria"

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  1. ; (, Ergodic Theory and Dynamical Systems)
    Abstract We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples are obtained by AbC constructions with several frequencies. 
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  2. ; (, Ergodic Theory and Dynamical Systems)
    Abstract Consider an analytic Hamiltonian system near its analytic invariant torus $$\mathcal T_0$$ carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $$\mathcal T_0$$ is convergent and has a particular form: it is an analytic function of its non-degenerate quadratic part. We prove that in this case there is an analytic canonical transformation—not just a formal power series—bringing the Hamiltonian into its Birkhoff normal form. 
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  3. ; (, Discrete & Continuous Dynamical Systems)
    Any \begin{document}$ C^d $$\end{document} conservative map \begin{document}$$ f $$\end{document} of the \begin{document}$$ d $$\end{document}-dimensional unit ball \begin{document}$$ {\mathbb B}^d $$\end{document}, \begin{document}$$ d\geq 2 $$\end{document}, can be realized by renormalized iteration of a \begin{document}$$ C^d $$\end{document} perturbation of identity: there exists a conservative diffeomorphism of \begin{document}$$ {\mathbb B}^d $$\end{document}, arbitrarily close to identity in the \begin{document}$$ C^d $$\end{document} topology, that has a periodic disc on which the return dynamics after a \begin{document}$$ C^d $$\end{document} change of coordinates is exactly \begin{document}$$ f $$\end{document}$. 
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  4. ; ; (, Electronic Journal of Probability)
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