Related papers: A note on a standard family of twist maps

The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some approachable one-parameter families of rational maps; the goal…

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

Since Moser's seminal work it is well known that the invariant curves of smooth nearly integrable twist maps of the cylinder with Diophantine rotation number are preserved under perturbation. In this paper we show that, in the analytic…

We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to…

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…

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…

We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On…

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…

Modular invariants of families of curves are Arakelov invariants in arithmetic algebraic geometry. All the known uniform lower bounds of these invariants are not sharp. In this paper, we aim to give explicit lower bounds of modular…

In this paper new numerical invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connections that occur when a separatrix loop of a hyperbolic saddle…

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…

We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.

In this article we investigate the fragility of invariant Lagrangian graphs for dissipative maps, focusing on their destruction under small perturbations. Inspired by Herman's work on conservative systems, we prove that all $C^0$-invariant…

In this paper we propose and study a new structural invariant for graphs, called distance-unbalanced\-ness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of…

We study Thurston equivalence classes of quadratic post-critically finite branched coverings. For these maps, we introduce and study invariant spanning trees. We give a computational procedure for searching for invariant spanning trees.…

The existence of translated curves for quasiperiodically forced maps is established, under very mild regularity hypotheses, for rotation numbers of constant type. Among the translated curves, the invariant curves are characterized as the…

We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…

We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by discretising the space of planar rotations. We let the angle of rotation approach $\pi/2$, and show that the limit of vanishing discretisation…

We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its…

In this note, we investigate the dynamics of invariant circles in area-preserving twist maps. The invariant circles under consideration lie beyond the applicability of classical KAM theory, as the perturbations involved exceed the scope of…