Related papers: Circle diffeomorphisms forced by expanding circle …
Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and `threshold' systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake…
Under a plausible geometric hypothesis, we show that a biholomorphic mapping of smoothly bounded, pseudoconvex domains extends to a diffeomorphism of the closures.
A topological constraint on the dynamics of a magnetic field in a flux tube arises from the fixed point indices of its field line mapping. This can explain unexpected behaviour in recent resistive-magnetohydrodynamic simulations of magnetic…
In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
The evolute of a plane curve is the envelope of its normals. Replacing the normals by the lines that make a fixed angle with the curve yields a new curve, called the evolutoid. We prefer the term ``skew evolute", and we study the geometry…
Inspired by examples of Katok and Milnor \cite{Milnor1997}, we construct simple examples of skew-product volume preserving diffeomorphism where the center foliation is pathological in the sense that, there is a full measure set whose…
We list all analytic diffeomorphisms between an open subset of the 4-dimensional projective space and an open subset of the 4-dimensional sphere that take all line segments to arcs of round circles. These are the following: restrictions of…
We describe the way in which the sign of the Schwarzian derivative for a family of diffeomorphisms of the interval $I$ affects the dynamics of an associated many-to-one skew product map of the cylinder $(\R/\Z)\times I$.
We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…
We consider skew-products with concave interval fiber maps over a certain subshift obtained as the projection of orbits staying in a given region. It generates a new type of (essentially) coded shift. The fiber maps have expanding and…
In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes…
We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branches. Assuming a topologically mixing condition and the…
Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical…
We study locally constant skew-product maps over full shifts of finite symbols with arbitrary compact metric spaces as fiber spaces. We introduce a new criterion to determine the density of leaves of the strong unstable (and strong stable)…
We study skew-products of the form $(x,u) \mapsto (fx, u + \varphi(x))$ where $f$ is a non-uniformly expanding map on a manifold $X$ and $\varphi: X \to \mathbb{S}^1$ is piecewise $\mathcal{C}^1$. If the systems satisfies mild assumptions…
We study contraction conditions for an iterated function system of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space,…
We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can…
We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph…
We give a heuristic method to solve explicitly for an absolutely continuous invariant measure for a piecewise differentiable, expanding map of a compact subset $I$ of Euclidean space $R^d$. The method consists of constructing a skew product…