Related papers: Monotone periodic orbits for torus homeomorphisms

Identity-homotopic self-homeomorphisms of a space of non-periodic 1-dimensional tiling are generalizations of orientation-preserving self-homeomorphisms of circles. We define the analogue of rotation numbers for such maps. In constrast to…

A torus manifold is an even-dimensional manifold acted on by a half-dimensional torus with non-empty fixed point set and some additional orientation data. It may be considered as a far-reaching generalisation of toric manifolds from…

We prove several generic existence results for infinitely many periodic orbits of Hamiltonian diffeomorphisms or Reeb flows. For instance, we show that a Hamiltonian diffeomorphism of a complex projective space or Grassmannian generically…

An orientation-preserving recurrent homeomorphism of the two-sphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

We study the non-wandering set of contracting Lorenz maps. We show that if such a map $f$ doesn't have any attracting periodic orbit, then there is a unique topological attractor. Precisely, there is a compact set $\Lambda$ such that…

By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…

We study a class of smooth torus manifolds whose orbit space has the combinatorial structure of a simple polytope with holes. We construct moment angle manifolds for such polytopes with holes and use them to prove that the associated torus…

We compare two formulas for the class of a generic torus orbit closure on the Grassmannian, due to Klyachko and Berget-Fink. The naturally emerging combinatorial objects are semi-standard fillings we call 1-strip-less tableaux.

In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological entropy. Here, we give a converselike theorem. We show that…

We prove the Conley conjecture for negative monotone, closed symplectic manifolds, i.e., the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of such manifolds.

A dynamical Mertens' theorem for ergodic toral automorphisms with error term O(N^{-1}) is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are found with many more, and with many fewer,…

We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves…

Newton famously showed that a gravitational force inversely proportional to the square of the distance, $F \sim 1/r^2$, formally explains Kepler's three laws of planetary motion. But what happens to the familiar elliptical orbits if the…

In this paper we consider $C^{1+\epsilon}$ area-preserving diffeomorphisms of the torus $f,$ either homotopic to the identity or to Dehn twists. We suppose that $f$ has a lift $\widetilde{f}$ to the plane such that its rotation set has…

Let $S$ be a closed surface of genus $g\geq 1$, furnished with an area form $\omega$. We show that there exists an open and dense set ${\mathcal O_r}$ of the space of Hamiltonian diffeomorphisms of class $C^r$, $1\leq r\leq\infty$, endowed…

Let $K_1$, $K_2$ $\subset$ $R^2$ be two convex, compact sets. We would like to know if there are commuting torus homeomorphisms $f$ and $h$ homotopic to the identity, with lifts $\tilde f$ and $\tilde h$, such that $K_1$ and $K_2$ are their…

We consider $C^{1+\epsilon}$ diffeomorphisms of the torus, denoted $f,$ homotopic to the identity and whose rotation sets have interior. We give some uniform bounds on the displacement of points in the plane under iterates of a lift of $f,$…

We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.

In this text we study billiards on ovals and investigate some consequences of a rotational symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits…