On a Bernoulli Property of some Piecewise C2-Diffeomorphisms in ...d.
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 one-dimensional analogue of the Smale horseshoe
We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.
On analytic invariant measures for expanding mappings
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 C2-Diffeomorphisms of the Circle which are of Type III1.
On discrete subgroups of Lie groups and elliptic geometric structures.
In this paper we continue the investigation of [7]-[10] concerning the actions of discrete subgroups of Lie groups on compact manifolds.
On Ergodic Averages for Affine Lattice Actions on Tori.
On fixed points of extensions of expanding maps in the unit disc
Using a result due to M. Shub, a theorem about the existence of fixed points inside the unit disc for extensions of expanding maps defined on the boundary is established. An application to a special class of rational maps on the Riemann sphere and some considerations on ergodic properties of these maps are also made.
On Generators for Ergodic Flowers.
On invariant measures for piecewise -transformations of the n-dimensional cube
On invariant measures for some infinite-dimensional dynamical systems
On invariant measures for the tend map.
The bifurcation structure of a one parameter dependent piecewise linear population model is described. An explicit formula is given for the density of the unique invariant absolutely continuous probability measure mub for each parameter value b. The continuity of the map b --> mub is established.
On iterations of Misiurewicz's rational maps on the Riemann sphere
On metric properties of substitutions
On small stochastic perturbations of mappings of the unit interval
On the algebraic hull of an automorphism group of a principal bundle.
On the dynamics of rational maps
On the Entropy of the Geodesic Flow in Manifolds Without Conjugate Points.
On the Ergodicity of Frame Flows.