The Rotating String.
The Ruelle rotation of Killing vector fields
We present an explicit formula for the Ruelle rotation of a nonsingular Killing vector field of a closed, oriented, Riemannian 3-manifold, with respect to Riemannian volume.
The second-order quadratic family.
The Semiclassical Electron in a Magnetic Field and Lattice. Some Problems of Low Dimensional "Periodic" Topology.
The semidynamical system near a closed negatively strongly invariant set.
The sequence entropy for Morse shifts and some counterexamples
The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos
We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
The simplest shadowing
Two different and easy proofs are presented that a hyperbolic linear homeomorphism of a Banach space admits the shadowing.
The singularities of Yang-Mills connections for bundles on a surface.
The size of scrambled sets: n-dimensional case
The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space
For n ≥ 1, given an n-dimensional locally (n-1)-connected compact space X and a finite Borel measure μ without atoms at isolated points, we prove that for a generic (in the uniform metric) continuous map f:X → X, the set of points which are chain recurrent under f has μ-measure zero. The same is true for n = 0 (skipping the local connectedness assumption).
The solution of general KdV equation in a class of steplike functions.
The space of morphisms on projective space
The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations
The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda -soliton is computed, using Sato theory. The result is used to give an explicit expansion of the fundamental solution of some discrete heat equations, in a series of Jackson’s -Bessel functions. For Askey-Wilson type solitons, this expansion reduces to a finite sum.
The Spectrum of Jacobi Matrices.
The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...
The stability of Nash-Cournot equilibria in labor managed oligopolies.
The ?-Stability Theorem for Flows.
The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial