Packing dimensions, transversal mappings and geodesic flows.
Leikas, Mika (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
Sylvain Crovisier, Martin Sambarino, Dawei Yang (2015)
Journal of the European Mathematical Society
We show that any diffeomorphism of a compact manifold can be approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.
Vanderlei Horita, Ali Tahzibi (2006)
Annales de l'I.H.P. Analyse non linéaire
C. A. Morales (2013)
Mathematica Bohemica
We study countable partitions for measurable maps on measure spaces such that, for every point , the set of points with the same itinerary as that of is negligible. We prove in nonatomic probability spaces that every strong generator (Parry, W., Aperiodic transformations and generators, J. London Math. Soc. 43 (1968), 191–194) satisfies this property (but not conversely). In addition, measurable maps carrying partitions with this property are aperiodic and their corresponding spaces are nonatomic....
Serge Troubetzkoy (2005)
Annales de l’institut Fourier
There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.
Mestel, B.D., Osbaldestin, A.H. (2000)
Mathematical Physics Electronic Journal [electronic only]
Papini, Duccio, Zanolin, Fabio (2002)
Georgian Mathematical Journal
Juan Luis García Guirao, Jaume Llibre (2008)
Colloquium Mathematicae
The aim of this paper is to describe the set of periods of a Morse-Smale diffeomorphism of the two-dimensional sphere according to its homotopy class. The main tool for proving this is the Lefschetz fixed point theory.
Hidalgo, M.C. (1992)
Acta Mathematica Universitatis Comenianae. New Series
Pierre Berger (2011)
Annales de l’institut Fourier
On se propose de montrer que les variétés à bord et plus généralement à coins, normalement dilatées par un endomorphisme sont persistantes en tant que stratifications -régulières. Ce résultat sera démontré en classe , pour . On donne aussi un exemple simple d’une sous-variété à bord normalement dilatée mais qui n’est pas persistante en tant que sous-variété différentiable.
Zeng, Chongchun (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Xavier Buff, Thomas Gauthier (2013)
Bulletin de la Société Mathématique de France
We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.
Neil Dobbs (2015)
Fundamenta Mathematicae
We use Pesin theory to study possible equilibrium measures for a broad class of piecewise monotone maps of the interval and a broad class of potentials.
Vadivasova, T.E., Sosnovtseva, O.V., Balanov, A.G., Astakhov, V.V. (2000)
Discrete Dynamics in Nature and Society
Erjaee, G.H., Alnasr, M. (2009)
Discrete Dynamics in Nature and Society
Vítor Araújo, Maria José Pacifico (2009)
Fundamenta Mathematicae
We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the...
Françoise Pène (2009)
Annales de l'I.H.P. Probabilités et statistiques
We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by the random variable...
Thierry Barbot (2001)
Annales scientifiques de l'École Normale Supérieure
Pedro Duarte (1994)
Annales de l'I.H.P. Analyse non linéaire
V. Khatskevich, L. Zelenko (2006)
Studia Mathematica
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...