Related papers: A condition that implies full homotopical complexi…

In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$-parameter isometry group. As an application of this result, we provide a new proof of the fact that every…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

We prove that, for any infinite-type surface $S$, the integral homology of the closure of the compactly-supported mapping class group $\overline{\mathrm{PMap}_c(S)}$ and of the Torelli group $\mathcal{T}(S)$ is uncountable in every positive…

We prove that a generic area-preserving diffeomorphism of a compact surface with non-empty boundary has an equidistributed set of periodic orbits. This implies that such a diffeomorphism has a dense set of periodic points, although we also…

Let $f: S^2 \to S^2$ be a postcritically finite branched covering map without periodic branch points. We give necessary and sufficient algebraic conditions for $f$ to be homotopic, relative to its postcritical set, to an expanding map $g$.

Let $H: \mathbb{R}^4 \to \mathbb{R}$ be any smooth function. This article introduces some arguments for extracting dynamical information about the Hamiltonian flow of $H$ from high-dimensional families of closed holomorphic curves. We work…

Let $\pi : \widetilde{\mathcal{N}} \to \mathcal{N}$ be a Riemannian covering, with $\mathcal{N}$, $\widetilde{\mathcal{N}}$ smooth compact connected Riemannian manifolds. If $\mathcal{M}$ is an $m$-dimensional compact simply-connected…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

We show that for any connected smooth manifold $M$ of dimension different from $3$ the restriction of the compact-open topology to the diffeomorphism group of $M$ is minimal, i.e. the group does not admit a strictly coarser Hausdorff group…

A well-known conjecture of Caratheodory states that the number of umbilic points on a closed convex surface in ${\mathbb E}^3$ must be greater than one. In this paper we prove this for $C^{3+\alpha}$-smooth surfaces. The Conjecture is first…

Fourier coefficients of automorphic representations $\pi$ of $\Sp_{2n}(\BA)$ are attached to unipotent adjoint orbits in $\Sp_{2n}(F)$, where $F$ is a number field and $\BA$ is the ring of adeles of $F$. We prove that for a given $\pi$, all…

We explicitly calculate the fundamental group of the space $\mathcal F$ of all immersed closed curves on a surface $F$. It is shown that $\pi_n(\mathcal F)=0$, n>1 for $F\neq S^2, RP^2$. It is also proved that $\pi_2(\mathcal F)=\Z$, and…

Given two semistable, non potentially isotrivial elliptic surfaces over a curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the…

We prove a generalization of the Poincar\'e-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the…

We prove that a homeomorphism of the torus homotopic to the identity whose rotation set is reduced to a single totally irrational vector is chain-recurrent. In fact, we show that pseudo-orbits can be chosen with a small number of jumps, in…

The purpose of this paper is to advance the knowledge of the dynamics arising from the creation and subsequent bifurcation of Poincar\'e heteroclinic cycles. The problem is central to dynamics: it has to be addressed if, for instance, one…

Motivated by the question whether a round disk can be realized as the rotation set of a torus diffeomorphism, we study the roundness of rotation sets of a parametric family of torus diffeomorphisms $F_\rho$, where the parameter $\rho$…

We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively…

Given a closed complex hypersurface $Z\subset \mathbb{C}^{N+1}$ $(N\in\mathbb{N})$ and a compact subset $K\subset Z$, we prove the existence of a pseudoconvex Runge domain $D$ in $Z$ such that $K\subset D$ and there is a complete proper…

We prove a conjecture of Teissier asserting that if $f$ has an isolated singularity at $P$ and $H$ is a smooth hypersurface through $P$, then $\widetilde{\alpha}_P(f)\geq \widetilde{\alpha}_P(f\vert_H)+\frac{1}{\theta_P(f)+1}$, where…