On a Bernoulli Property of some Piecewise C2-Diffeomorphisms in ...d.
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Piotr Bugiel (1993)
Monatshefte für Mathematik
Grzegorz Świrszcz (1998)
Fundamenta Mathematicae
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.
Ryszard Rudnicki (1991)
Annales Polonici Mathematici
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.
K. Krzyżewski (1982)
Colloquium Mathematicae
Konstantin Medynets (2007)
Fundamenta Mathematicae
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...
Klaus Schmidt, Jane Hawkins (1982)
Inventiones mathematicae
Robert J. Zimmer (1985)
Revista Matemática Iberoamericana
In this paper we continue the investigation of [7]-[10] concerning the actions of discrete subgroups of Lie groups on compact manifolds.
S.G. Dani, S. Muralidharan (1983)
Monatshefte für Mathematik
Roberto Tauraso (1994)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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.
Christian Grillenberger (1980)
Mathematische Zeitschrift
M. Jabłoński (1983)
Annales Polonici Mathematici
P. E. Zhidkov (1995)
Annales de l'I.H.P. Physique théorique
Francesc Bofill (1988)
Stochastica
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.
P. Grzegorczyk, F. Przytycki, W. Szlenk (1990)
Annales de l'I.H.P. Physique théorique
Mariusz Lemańczyk, Mieczystaw K. Mentzen (1988)
Compositio Mathematica
Paweł Góra (1984)
Colloquium Mathematicae
Robert J. Zimmer (1990)
Commentarii mathematici Helvetici
R. Mañé, P. Sad, D. Sullivan (1983)
Annales scientifiques de l'École Normale Supérieure
A. Freire, R. Mane (1982)
Inventiones mathematicae
M. Brin, M. Gromov (1980)
Inventiones mathematicae
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