On algebraic Anosov diffeomorphisms on nilmanifolds.
On algebraic sets invariant by one-dimensional foliations on
We consider the problem of extending the result of J.-P. Jouanolou on the density of singular holomorphic foliations on without algebraic solutions to the case of foliations by curves on . We give an example of a foliation on with no invariant algebraic set (curve or surface) and prove that a dense set of foliations admits no invariant algebraic set.
On almost specification and average shadowing properties
We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in...
On an analytic approach to the Fatou conjecture
Let f be a quadratic map (more generally, , d > 1) of the complex plane. We give sufficient conditions for f to have no measurable invariant linefields on its Julia set. We also prove that if the series converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.
On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation.
On an invariance principle for phase separation lines
On analytic flows on the torus which are disjoint from systems of probabilistic origin
We describe two methods of obtaining analytic flows on the torus which are disjoint from dynamical systems induced by some classical stationary processes.
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