Obtuse triangular billiards. I: Near the triangle.
On a certain map of a triangle
The paper answers some questions asked by Sharkovski concerning the map F:(u,v) ↦ (u(4-u-v),uv) of the triangle Δ = u,v ≥ 0: u+v ≤ 4. We construct an absolutely continuous σ-finite invariant measure for F. We also prove the following strange phenomenon. The preimages of side I = Δ ∩ v=0 form a dense subset of Δ and there is another dense set Λ consisting of points whose orbits approach the interval I but are not attracted by I.
On a class of continuous flow.
On a function related to the continued fraction transformation
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 invariance principle for phase separation lines
On circle map coupled map lattice.
On codimension one submersions of euclidean spaces.
On commuting properties of endomorphisms of formal A-modules over finite fields
On conjugacy equation in dimension one
In this paper, recent results on the existence and uniqueness of (continuous and homeomorphic) solutions φ of the equation φ ∘ f = g ∘ φ (f and g are given self-maps of an interval or the circle) are surveyed. Some applications of these results as well as the outcomes concerning systems of such equations are also presented.
On cycles and orbits of polynomial mappings
On diffeomorphisms with polynomial growth of the derivative on surfaces
We consider zero entropy -diffeomorphisms on compact connected -manifolds. We introduce the notion of polynomial growth of the derivative for such diffeomorphisms, and study it for diffeomorphisms which additionally preserve a smooth measure. We show that if a manifold M admits an ergodic diffeomorphism with polynomial growth of the derivative then there exists a smooth flow with no fixed point on M. Moreover, if dim M = 2, then necessarily M = ² and the diffeomorphism is -conjugate to a skew...
On disjointness properties of some smooth flows
Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval exchange...
On geometric detection of periodic solutions and chaotic dynamics.
On homoclinic solutions of a semilinear -Laplacian difference equation with periodic coefficients.
On Irwin's proof of the pseudostable manifold theorem.
On local first order structural stability of pairings of vector fields and functions
On maximal transitive sets of generic diffeomorphisms