The reduction of symplectic structure and Sternberg construction
The Reidemeister zeta function and the computation of the Nielsen zeta function
The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation.
The return sequence of the Bowen-Series map for punctured surfaces
For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the Liouville measure. ...
The Riccati equation: pinching of forcing and solutions.
The role of delay in digestion of plankton by fish population: A fishery model.
The role of the incubation period in a disease model.
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.