Related papers: Homotopically unbounded disks for generic surface …

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…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

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

We characterise boundary shaped disc like neighbourhoods of certain isotropic submanifolds in terms of aperiodicity of Reeb flows. We prove uniqueness of homotopy and diffeomorphism type of such contact manifolds assuming non-existence of…

We study homotopic-to-the-identity torus homeomorphisms, whose rotation set has nonempty interior. We prove that any such map is monotonically semiconjugate to a homeomorphism that preserves the Lebesgue measure, and that has the same…

We show that for generic homeomorphisms homotopic to the identity in a closed and oriented surface of genus $g>1$, the rotation set is given by a union of at most $2^{5g-3}$ convex sets. Examples showing the sharpness for this asymptotic…

It is well-known that there is a close relationship between the dynamics of diffeomorphisms satisfying the axiom $A$ and the topology of the ambient manifold. In the given article, this statement is considered for the class $\mathbb G(M^2)$…

Let $f$ be a transitive homeomorphism of the two-dimensional torus in the homotopy class of the identity. We show that a lift of $f$ to the universal covering is transitive if and only if the rotation set of the lift contains the origin in…

The first main result is a topological rigidity theorem for complete immersed hypersurfaces of spherical space forms which extends similar results due to do Carmo/Warner, Wang/Xia and Longa/Ripoll. Under certain sharp conditions on the…

Let $f$ be an $R$-closed homeomorphism on a connected orientable closed surface $M$. In this paper, we show that If $M$ has genus more than one, then each minimal set is either a periodic orbit or an extension of a Cantor set. If $M =…

Expanding on work by Conway, Orson, and Powell, we study the isotopy classes rel. boundary of nonorientable, compact, locally flatly embedded surfaces in $D^4$ with knot group $\mathbb{Z}_2$. In particular we show that if two such surfaces…

We study Hamiltonian diffeomorphisms of closed symplectic manifolds with non-contractible periodic orbits. In a variety of settings, we show that the presence of one non-contractible periodic orbit of a Hamiltonian diffeomorphism of a…

In this paper we consider $C^\infty $-generic families of area-preserving diffeomorphisms of the torus homotopic to the identity and their rotation sets. Let $f_t:\rm{T^2\rightarrow T^2}$ be such a family, $\widetilde{f}_t:\rm…

We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the…

We prove that a real analytic pseudo-rotation $f$ of the disc or the sphere is never topologically mixing. When the rotation number of $f$ is of Brjuno type, the latter follows from a KAM theorem of R\"ussmann on the stability of real…

We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two non-compact orientable surfaces is a proper map, then it is…

We investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit converges to a periodic orbit and, moreover, that there exists…

Let $S$ be a closed surface of genus $g\geq 2$, furnished with a Borel probability measure $\lambda$ with total support. We show that if $f$ is a $\lambda$-preserving homeomorphism isotopic to the identity such that the rotation vector…

Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by…

We construct a $C^\infty$ area-preserving diffeomorphism of the two-dimensional torus which is Bernoulli (in particular, ergodic) with respect to Lebesgue measure, homotopic to the identity, and has a lift to the universal covering whose…