On holomorphic foliations without algebraic solutions.
On homoclinic solutions of a semilinear -Laplacian difference equation with periodic coefficients.
On implicit Lagrangian differential systems
Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).
On inertial manifolds for reaction-diffusion equations on genuinely high-dimensional thin domains
We study a family of semilinear reaction-diffusion equations on spatial domains , ε > 0, in lying close to a k-dimensional submanifold ℳ of . As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by . The definition of , given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable characterizations...
On inhomogeneous self-similar measures and their spectra
Let for i = 1,..., N be contracting similarities, let be a probability vector and let ν be a probability measure on with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure μ on such that . We give satisfactory estimates for the lower and upper bounds of the spectra of inhomogeneous self-similar measures. The case in which there are a countable number of contracting similarities and probabilities is considered. In particular, we...
On integrability of a special class of two-component (2+1)-dimensional hydrodynamic-type systems.
On invariant measures for piecewise -transformations of the n-dimensional cube
On invariant measures for some infinite-dimensional dynamical systems
On invariant measures for the tend map.
The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mub for each parameter value b. The continuity of the map b --> mub is established.
On invariant tori of nearly integrable Hamiltonian systems with quasiperiodic perturbation.
On Irwin's proof of the pseudostable manifold theorem.
On isomorphism of integrable cases of the Euler equations on the bi-Hamiltonian manifolds and .
On iterated torus knots and transversal knots.
On iterates of strong Feller operators on ordered phase spaces
Let (X,d) be a metric space where all closed balls are compact, with a fixed σ-finite Borel measure μ. Assume further that X is endowed with a linear order ⪯. Given a Markov (regular) operator P: L¹(μ) → L¹(μ) we discuss the asymptotic behaviour of the iterates Pⁿ. The paper deals with operators P which are Feller and such that the μ-absolutely continuous parts of the transition probabilities are continuous with respect to x. Under some concentration assumptions on the asymptotic transition probabilities...
On iterations of Misiurewicz's rational maps on the Riemann sphere
On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation
We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng and a recent...
On Lagrange epimorphisms and Lagrange submersions.
On limiting directions of Julia sets.
On linguistic dynamical systems, families of graphs of large girth, and cryptography.
On local aspects of topological weak mixing in dimension one and beyond
We introduce the concept of weakly mixing sets of order n and show that, in contrast to weak mixing of maps, a weakly mixing set of order n does not have to be weakly mixing of order n + 1. Strictly speaking, we construct a minimal invertible dynamical system which contains a non-trivial weakly mixing set of order 2, whereas it does not contain any non-trivial weakly mixing set of order 3. In dimension one this difference is not that much visible, since we prove that every continuous...