An existence result on periodic solutions of an ordinary -Laplacian system.
An exotic flow on a compact surface
In 1988 Anosov [1] published the construction of an example of a flow (continuous real action) on a cylinder or annulus with a phase portrait strikingly different from our normal experience. It contains orbits whose -limit sets contain a non-periodic orbit along with a simple closed curve of fixed points, but these orbits do not wrap down on this simple closed curve in the usual way. In this paper we modify some of Anosov’s methods to construct a flow on a surface of genus with equally striking...
An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.
An explicit separate solution for the Tzitzeica equation.
An exponential estimate for convolution powers
We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
An extension of Markov partitions for a certain toral endomorphism.
An extension of the Artin-Mazur theorem.
An extension of the Khinchin-Groshev theorem
We prove a version of the Khinchin-Groshev theorem in Diophantine approximation for quadratic extensions of function fields in positive characteristic.
An extension which is relatively twofold mixing but not threefold mixing
We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
An implementation of the Bestvina-Handel algorithm for surface homeomorphisms.
An index for global Hopf bifurcation in parabolic systems.
An Index Theory and Existence of Multiple Brake Orbits for Star-Shaped Hamiltonian Systems
An inertial manifold and the principle of spatial averaging.
An infinite level atom coupled to a heat bath.
An integrable flow on a family of Hilbert Grassmannians.
An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control
Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data. We analyze a non-linear model of the human immunodeficiency virus (HIV)...
An introduction to probabilistic methods with applications
This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics....
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
An -theory of the generalized Stokes resolvent system in infinite cylinders
Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.
An ordered structure of rank two related to Dulac's Problem
For a vector field ξ on ℝ² we construct, under certain assumptions on ξ, an ordered model-theoretic structure associated to the flow of ξ. We do this in such a way that the set of all limit cycles of ξ is represented by a definable set. This allows us to give two restatements of Dulac’s Problem for ξ - that is, the question whether ξ has finitely many limit cycles-in model-theoretic terms, one involving the recently developed notion of -rank and the other involving the notion of o-minimality.