Eugen Mihailescu
Entropy production and folding of the phase space in chaotic dynamics.
Thu, 04/14/2011 - 15:01 — SomNambulAuthors: Eugen Mihailescu
Subjects: Dynamical Systems
AbstractWe study the entropy production of Gibbs (equilibrium) measures for chaotic
dynamical systems with folding of the phase space. The dynamical chaotic model
is that generated by a hyperbolic non-invertible map $f$ on a general basic
(possibly fractal) set $\Lambda$; the non-invertibility creates new phenomena
and techniques than in the diffeomorphism case. We prove a formula for the
\textit{entropy production}, involving an asymptotic logarithmic degree, with
respect to the equilibrium measure $\mu_\phi$ associated to the potential
$\phi$.Isomorphism classes for certain expanding maps and their group extensions.
Mon, 02/14/2011 - 16:01 — SomNambulAuthors: Eugen Mihailescu
Subjects: Dynamical Systems
AbstractWe show that expanding toral endomorphisms, together with their respective
Lebesgue measure are isomorphic to 1-sided Bernoulli shifts. This result is
then extended to smooth perturbations of expanding toral endomorphisms,
together with their respective measures of maximal entropy. Also we study group
extensions of expanding toral endomorphisms and show that under certain, not
too restrictive conditions on the extension cocycle, these skew products are
1-sided Bernoulli as well.On a class of stable conditional measures for endomorphisms.
Fri, 02/26/2010 - 16:01 — SomNambulAuthors: Eugen Mihailescu
Subjects: Dynamical Systems
AbstractWe study stable conditional measures for a certain equilibrium measure for
hyperbolic endomorphisms, on basic sets with overlaps; we show that these
conditional measures are geometric probabilities and measures of maximal stable
dimension. They are also proved to be absolutely continuous if and only if the
respective basic set is a folded repellor. Examples of such non-reversible
systems and their associated measures are given too.Unstable directions and dimension for a class of skew products with overlaps.
Fri, 11/13/2009 - 16:01 — SomNambulAuthors: Eugen Mihailescu
Subjects: Dynamical Systems
AbstractWe study a class of skew products with overlaps in fibers and show that in
this case the unstable manifolds really depend on prehistories, even for
perturbations of the original maps. We also give several results about the
Hausdorff dimension of the fibers of the respective locally maximal invariant
set, by using the inverse pressure, the thickness of Cantor sets and some
bounds for the preimage counting function.Invariant measures involving local inverse iterates.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Eugen Mihailescu
Subjects: Dynamical Systems
AbstractWe study some new invariant measures arising from local inverse iterates.
Examples are also given.
User login
