A lambda-graph system for the Dyck shift and its -groups.
A lattice gas model for the incompressible Navier–Stokes equation
We recover the Navier–Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier–Stokes equation in a fixed time interval. The proof does not use nongradient methods or the multi-scale analysis due to the long range jumps.
A lemma and a conjecture on the cost of rearrangements
A Lie connection between Hamiltonian and Lagrangian optics.
A limit formula for regular iteration groups.
A limit formula for regular iteration groups. (Summary).
A limit set trichotomy for order-preserving systems on time scales.
A linear condition determining local or global existence for nonlinear problems
Given a nonlinear autonomous system of ordinary or partial differential equations that has at least local existence and uniqueness, we offer a linear condition which is necessary and sufficient for existence to be global. This paper is largely concerned with numerically testing this condition. For larger systems, principals of computations are clear but actual implementation poses considerable challenges. We give examples for smaller systems and discuss challenges related to larger systems. This...
A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs
For large N, we consider the ordinary continued fraction of x=p/q with 1≤p≤q≤N, or, equivalently, Euclid’s gcd algorithm for two integers 1≤p≤q≤N, putting the uniform distribution on the set of p and qs. We study the distribution of the total cost of execution of the algorithm for an additive cost function c on the set ℤ+* of possible digits, asymptotically for N→∞. If c is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named author....
A local-global criterion for dynamics on ℙ¹
A locally commutative free group acting on the plane
The purpose of this paper is to prove the existence of a free subgroup of the group of all affine transformations on the plane with determinant 1 such that the action of the subgroup is locally commutative.
A look on some results about Camassa–Holm type equations
We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.
A map maintaining the orbits of a given -action
Giordano et al. (2010) showed that every minimal free -action of a Cantor space X is orbit equivalent to some ℤ-action. Trying to avoid the K-theory used there and modifying Forrest’s (2000) construction of a Bratteli diagram, we show how to define a (one-dimensional) continuous and injective map F on X∖one point such that for a residual subset of X the orbits of F are the same as the orbits of a given minimal free -action.
A matrix formalism for conjugacies of higher-dimensional shifts of finite type
We develop a natural matrix formalism for state splittings and amalgamations of higher-dimensional subshifts of finite type which extends the common notion of strong shift equivalence of ℤ⁺-matrices. Using the decomposition theorem every topological conjugacy between two -shifts of finite type can thus be factorized into a finite chain of matrix transformations acting on the transition matrices of the two subshifts. Our results may be used algorithmically in computer explorations on topological...
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
A model of cardiac tissue as an excitable medium with two interacting pacemakers having refractory time
A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase.
A modified strong squeezing property and the existence of inertial manifolds of semiflows
A natural occurrence of shift equivalence
A natural occcurrence of shift equivalence in a purely algebraic setting is exhibited.
A necessary and sufficient condition for the existence of an exponential attractor
We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.
A new adaptive local linear prediction method and its application in hydrological time series.