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Award ID contains: 2101464

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  1. ; ; ; (, Nonlinearity)
    Abstract We consider two interacting particles on the circle. The particles are subject to stochastic forcing, which is modeled by white noise. In addition, one of the particles is subject to friction, which models energy dissipation due to the interaction with the environment. We show that, in the diffusive limit, the absolute value of the velocity of the other particle converges to the reflected Brownian motion. In other words, the interaction between the particles is asymptotically negligible in the scaling limit. The proof combines averaging for large energies with large deviation estimates for small energies. 
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    Free, publicly-accessible full text available April 11, 2026
  2. ; (, Communications in Mathematical Physics)
    Abstract We prove rotations-reducibility for close to constant quasi-periodic$$SL(2,\mathbb {R})$$ S L ( 2 , R ) cocycles in one frequency in the finite regularity and smooth cases, and derive some applications to quasi-periodic Schrödinger operators. 
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  3. ; ; (, Advances in Mathematics)
    We construct a smooth area preserving flow on a genus 2 surface with exactly one open uniquely ergodic component, that is asymmetrically bounded by separatrices of non-degenerate saddles and that is nevertheless not mixing. 
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    Free, publicly-accessible full text available April 1, 2026
  4. ; ; (, Journal de l’École polytechnique — Mathématiques)
    We construct conservative smooth flows of zero metric entropy which satisfy the classical central limit theorem. 
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  5. ; ; (, Discrete and Continuous Dynamical Systems)
    We give an example of a real analytic reparametrization of a minimal translation flow on $$\mathbb{T}^{5}$$ that has a Lebesgue spectrum with infinite multiplicity. As a consequence, we see that the dynamics on a non-Diophantine invariant torus of an almost integrable Hamiltonian system can be spectrally equivalent to a Bernoulli flow. 
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  6. ; (, Journal of the European Mathematical Society)
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  7. ; (, Ergodic Theory and Dynamical Systems)
    Abstract We construct a $C^1$ symplectic twist map g of the annulus that has an essential invariant curve $$\Gamma $$ such that $$\Gamma $$ is not differentiable and g restricted to $$\Gamma $$ is minimal. 
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  8. ; (, 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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  9. (, Journal of the American Mathematical Society)
    A new diffusion mechanism from the neighborhood of elliptic equilibria for Hamiltonian flows in three or more degrees of freedom is introduced. We thus obtain explicit real entire Hamiltonians on R 2 d \mathbb {R}^{2d} , d ≥ 4 d\geq 4 , that have a Lyapunov unstable elliptic equilibrium with an arbitrary chosen frequency vector whose coordinates are not all of the same sign. For non-resonant frequency vectors, our examples all have divergent Birkhoff normal form at the equilibrium. On R 4 \mathbb {R}^4 , we give explicit examples of real entire Hamiltonians having an equilibrium with an arbitrary chosen non-resonant frequency vector and a divergent Birkhoff normal form. 
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  10. ; (, 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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