The Poincaré-Bendixson Theorem: from Poincaré to the XXIst century
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.
The power-law formalism as a tool for modeling hormonal systems.
The pressure of functions over -extensions.
The Prime Orbit Theorem for Quasihyperbolic Toral Automorphisms.
The rate of convergence for iterated function systems
Iterated function systems with place-dependent probabilities are considered. It is shown that the rate of convergence of transition probabilities to a unique invariant measure is geometric.
The real 3x+1 problem
The real-analytic solutions of the Abel functional equation
For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.
The recurrence dimension for piecewise monotonic maps of the interval
We investigate a weighted version of Hausdorff dimension introduced by V. Afraimovich, where the weights are determined by recurrence times. We do this for an ergodic invariant measure with positive entropy of a piecewise monotonic transformation on the interval , giving first a local result and proving then a formula for the dimension of the measure in terms of entropy and characteristic exponent. This is later used to give a relation between the dimension of a closed invariant subset and a pressure...
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.