A parabolic-hyperbolic system modelling a moving cell.
A partial generalization of Diliberto’s theorem for certain DEs of higher dimension
A perfect hashing incremental scheme for unranked trees using pseudo-minimal automata
We describe a technique that maps unranked trees to arbitrary hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to other hashing techniques based on automata, our procedure builds a pseudo-minimal DTA for this purpose. A pseudo-minimal automaton may be larger than the minimal one accepting the same language but, in turn, it contains proper elements (states or transitions which are unique) for every input accepted by the automaton. Therefore, pseudo-minimal DTA...
A planar integral self-affine tile with Cantor set intersections with its neighbors.
A Poincaré formula for the fixed point indices of the iterates of arbitrary planar homeomorphisms.
A polynomial class of Markus-Yamabe counterexamples.
In the paper [CEGHM] a polynomial counterexample to the Markus-Yamabe Conjecture and to the discrete Markus-Yamabe Question in dimension n ≥ 3 are given. In the present paper we explain a way for obtaining a family of polynomial counterexamples containing the above ones. Finally we study the global dynamics of the examples given in [CEGHM].
A prey-predator model with a cover linearly varying with the prey population and an alternative food for the predator.
A priori bounds for some infinitely renormalizable quadratics: II. Decorations
A decoration of the Mandelbrot set is a part of cut off by two external rays landing at some tip of a satellite copy of attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials satisfying the decoration condition, which means that the combinatorics of the renormalization operators involved is selected from a finite family of decorations. For this class of maps we provea priori bounds. They imply local connectivity of the corresponding Julia sets...
A probabilistic and geometric perspective.
A projectively natural flow for circle diffeomorphisms.
A proof existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems.
A Proof of Simultaneous Linearization with a Polylog Estimate
We give an alternative proof of simultaneous linearization recently shown by T. Ueda, which connects the Schröder equation and the Abel equation analytically. In fact, we generalize Ueda's original result so that we may apply it to the parabolic fixed points with multiple petals. As an application, we show a continuity result on linearizing coordinates in complex dynamics.
A proof of the stability conjecture
A property of connections of mechanical systems of higher order
A property of ergodic flows
We introduce a property of ergodic flows, called Property B. We prove that an ergodic hyperfinite equivalence relation of type III₀ whose associated flow has this property is not of product type. A consequence is that a properly ergodic flow with Property B is not approximately transitive. We use Property B to construct a non-AT flow which-up to conjugacy-is built under a function with the dyadic odometer as base automorphism.
A quantified Tauberian theorem for sequences
The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson-Tzafriri theorem recently obtained by the author...
A quantitative ergodic theory proof of Szemerédi's theorem.
A quantum particle in a quadrupole radio-frequency trap
A ratio ergodic theorem for multiparameter non-singular actions
We prove a ratio ergodic theorem for non-singular free and actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in . The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general group...
A reaction-diffusion equation on a net-shaped thin domain