Related papers: $C^0$-rigidity of Poisson diffeomorphisms

We consider deformations of a group of circle diffeomorphisms with H\"older continuous derivatives in the framework of quasiconformal Teichm\"uller theory and show certain rigidity under conjugation by symmetric homeomorphisms of the…

We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…

In this paper we introduce a new method for approaching the C^0 - rigidity results for the Poisson bracket. Using this method, we provide a different proof for the lower semi-continuity under C^0 perturbations, for the uniform norm of the…

An anologue of the Calabi invariant for Poisson manifolds is considered. For any Poisson manifold $P$, the Poisson bracket on $C^{\infty}(P)$ extends to a Lie bracket on the space $\Omega^{1}(P)$ of all differential one-forms, under which…

This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of…

Let (M, {\pi} ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives rise to an algebroid $AP \rightarrow P$, to which we associate certain chomology groups which control formal deformations of {\pi} around P . Assuming that these…

We construct explicitly a class of coboundary Poisson-Lie structures on the group of formal diffeomorphisms of ${\Bbb R}^n$. Equivalently, these give rise to a class of coboundary triangular Lie bialgebra structures on the Lie algebra $W_n$…

Asaoka & Irie recently proved a $C^{\infty}$ closing lemma of Hamiltonian diffeomorphisms of closed surfaces. We reformulated their techniques into a more general perturbation lemma for area-preserving diffeomorphism and proved a…

In this work we completely classify $C^\infty$ conjugacy for conservative partially hyperbolic diffeomorphisms homotopic to a linear Anosov automorphism on the 3-torus by its center foliation behavior. We prove that the uniform version of…

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…

In this paper, we present a $C^0$-fragmentation property for Hamiltonian diffeomorphisms. More precisely, it is known that for a given open covering $\mathcal{U}$ of a compact symplectic surface we can write each $C^0$-small enough…

In this paper we prove that every homeomorphism of a compact metric space admitting an invariant probability measure with full support can be approximated in the $C^0$-Gromov--Hausdorff topology by homeomorphisms with zero topological…

We define cusp-decomposable manifolds and prove smooth rigidity within this class of manifolds. These manifolds generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume,…

Poisson structures vanishing linearly on a set of smooth closed disjoint curves are generic in the set of all Poisson structures on a compact connected oriented surface. We construct a complete set of invariants classifying these structures…

We compute the formal Poisson cohomology groups of a real Poisson structure $\pi$ on $\mathbb{C}^2$ associated to the Lefschetz singularity $(z_1, z_2)\mapsto z_1^2+z_2^2$. In particular we correct an erroneous computation in the…

Let $\Sigma$ be a surface equipped with an area form. There is an long standing open question by Katok, which, in particular, asks whether every entropy-zero Hamiltonian diffeomorphism of a surface lies in the $C^0$-closure of the set of…

We give a uniform construction that, on input of a recursive presentation $P$ of a group, outputs a recursive presentation of a torsion-free group, isomorphic to $P$ whenever $P$ is itself torsion-free. We use this to re-obtain a known…

In this paper we study $C^1$-structurally stable diffeomorphisms, that is, $C^1$ Axiom A diffeomorphisms with the strong transversality condition. In contrast to the case of dynamics restricted to a hyperbolic basic piece, structurally…

Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class ({\em i.e.} between $C^1$ and $C^2$). In particular, we demonstrate…

We prove that the entropy norm on the group of diffeomorphisms of a closed orientable surface of positive genus is unbounded.