On analytic invariant measures for expanding mappings
On Anosov energy levels of convex Hamiltonian systems.
On approximation of homeomorphisms of a Cantor set
We continue the study of topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ, which was started by Bezuglyi, Dooley, Kwiatkowski and Medynets. We prove that the set of periodic homeomorphisms is τ-dense in Homeo(X) and deduce from this result that the topological group (Homeo(X),τ) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugacy class is τ-dense in Homeo(X). We also show that for any homeomorphism...
On approximation of solutions to some -dimensional integrable systems by Bäcklund transformations.
On Arnold's conjecture for symplectic fixed points
On asymptotic stability of solitary waves for nonlinear Schrödinger equations
On backward stability of holomorphic dynamical systems
For a polynomial with one critical point (maybe multiple), which does not have attracting or neutral periodic orbits, we prove that the backward dynamics is stable provided the Julia set is locally connected. The latter is proved to be equivalent to the non-existence of a wandering continuum in the Julia set or to the shrinking of Yoccoz puzzle-pieces to points.
On biaccessible points in Julia sets of polynomials
Let f be a polynomial of one complex variable so that its Julia set is connected. We show that the harmonic (Brolin) measure of the set of biaccessible points in J is zero except for the case when J is an interval.
On boundaries of parallelizable regions of flows of free mappings.
On boundary homeomorphisms of trans-quasiconformal maps of the disk.
On -closeness of invariant foliations under numerics.
On C2-Diffeomorphisms of the Circle which are of Type III1.
On certain algebraic curves related to polynomial maps
On certain statistical properties of continued fractions with even and with odd partial quotients
On certain weighted moving averages and their differentiation analogues.
On chaotic dynamics in rational polygonal billiards.
On Chaotic Subthreshold Oscillations in a Simple Neuronal Model
In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.
On characterization of the solution set in case of generalized semiflow
In the paper, a possible characterization of a chaotic behavior for the generalized semiflows in finite time is presented. As a main result, it is proven that under specific conditions there is at least one trajectory of generalized semiflow, which lies inside an arbitrary covering of the solution set. The trajectory mutually connects each subset of the covering. A connection with symbolic dynamical systems is mentioned and a possible numerical method of analysis of dynamical behavior is outlined....
On circle map coupled map lattice.
On classical dynamics of affinely-rigid bodies subject to the Kirchhoff-Love constraints.