260 research outputs found
A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems
In this paper we introduce a new kind of Lax-Oleinik type operator with
parameters associated with positive definite Lagrangian systems for both the
time-periodic case and the time-independent case. On one hand, the new family
of Lax-Oleinik type operators with an arbitrary as
initial condition converges to a backward weak KAM solution in the
time-periodic case, while it was shown by Fathi and Mather that there is no
such convergence of the Lax-Oleinik semigroup. On the other hand, the new
family of Lax-Oleinik type operators with an arbitrary
as initial condition converges to a backward weak KAM solution faster than the
Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some
reference
Dominated Splitting and Pesin's Entropy Formula
Let be a compact manifold and be a diffeomorphism on
. If is an -invariant probability measure which is absolutely
continuous relative to Lebesgue measure and for
there is a dominated splitting on its orbit ,
then we give an estimation through Lyapunov characteristic exponents from below
in Pesin's entropy formula, i.e., the metric entropy satisfies
where
and
are the Lyapunov
exponents at with respect to Consequently, by using a dichotomy for
generic volume-preserving diffeomorphism we show that Pesin's entropy formula
holds for generic volume-preserving diffeomorphisms, which generalizes a result
of Tahzibi in dimension 2
On the number of Mather measures of Lagrangian systems
In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact
the minimizers of a "universal" infinite dimensional linear programming
problem. This fundamental result has many applications, one of the most
important is to the estimates of the generic number of Mather measures.
Ma\~n\'e obtained the first estimation of that sort by using finite dimensional
approximations. Recently, we were able with Gonzalo Contreras to use this
method of finite dimensional approximation in order to solve a conjecture of
John Mather concerning the generic number of Mather measures for families of
Lagrangian systems. In the present paper we obtain finer results in that
direction by applying directly some classical tools of convex analysis to the
infinite dimensional problem. We use a notion of countably rectifiable sets of
finite codimension in Banach (and Frechet) spaces which may deserve independent
interest
Persistent Chaos in High Dimensions
An extensive statistical survey of universal approximators shows that as the
dimension of a typical dissipative dynamical system is increased, the number of
positive Lyapunov exponents increases monotonically and the number of parameter
windows with periodic behavior decreases. A subset of parameter space remains
in which topological change induced by small parameter variation is very
common. It turns out, however, that if the system's dimension is sufficiently
high, this inevitable, and expected, topological change is never catastrophic,
in the sense chaotic behavior is preserved. One concludes that deterministic
chaos is persistent in high dimensions.Comment: 4 pages, 3 figures; Changes in response to referee comment
Entropy and Poincar\'e recurrence from a geometrical viewpoint
We study Poincar\'e recurrence from a purely geometrical viewpoint. We prove
that the metric entropy is given by the exponential growth rate of return times
to dynamical balls. This is the geometrical counterpart of Ornstein-Weiss
theorem. Moreover, we show that minimal return times to dynamical balls grow
linearly with respect to its length. Finally, some interesting relations
between recurrence, dimension, entropy and Lyapunov exponents of ergodic
measures are given.Comment: 11 pages, revised versio
Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
We describe the topological behavior of typical orbits of complex quadratic
polynomials P_alpha(z)=e^{2\pi i alpha} z+z^2, with alpha of high return type.
Here we prove that for such Brjuno values of alpha the closure of the critical
orbit, which is the measure theoretic attractor of the map, has zero area. Then
combining with Part I of this work, we show that the limit set of the orbit of
a typical point in the Julia set is equal to the closure of the critical orbit.Comment: 38 pages, 5 figures; fixed the issues with processing the figure
Lipschitz shadowing implies structural stability
We show that the Lipschitz shadowing property of a diffeomorphism is
equivalent to structural stability. As a corollary, we show that an expansive
diffeomorphism having the Lipschitz shadowing property is Anosov.Comment: 11 page
Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts
We consider continuous -cocycles over a strictly ergodic
homeomorphism which fibers over an almost periodic dynamical system
(generalized skew-shifts). We prove that any cocycle which is not uniformly
hyperbolic can be approximated by one which is conjugate to an
-cocycle. Using this, we show that if a cocycle's homotopy
class does not display a certain obstruction to uniform hyperbolicity, then it
can be -perturbed to become uniformly hyperbolic. For cocycles arising
from Schr\"odinger operators, the obstruction vanishes and we conclude that
uniform hyperbolicity is dense, which implies that for a generic continuous
potential, the spectrum of the corresponding Schr\"odinger operator is a Cantor
set.Comment: Final version. To appear in Duke Mathematical Journa
Clinical haematology of the great bustard (Otis tarda)
The haematological parameters of healthy great bustards (Otis tarda L.) have been determined. The values obtained were red cell count (3.0 x 10(12) +/- 0.2 x 10(12/)1), white cell count (33.0 x 10(9) +/- 2.6 x 10(9)/1), haematocrit value (0.51 +/- 0.01 1/1), haemoglobin (13.0 +/- 0.3 g/dl), mean corpuscular volume (178.7 +/- 12.5 fl), mean cell haemoglobin concentration (25.0 +/- 0.6 g/dl), mean corpuscular haemoglobin (42.5 +/- 3.2 pg), differential white cell count: heterophils (22.5 x 10(9) +/- 0.7 x 10(9)/1), lymphocytes (6.0 x 10(9)+/-0.7 x 10(9)/1), eosinophils (2.7 x 10(9) +/- 0.3 x 10(9)/1) and monocytes (1.8 x 10(9)+/-0.2 x 10(9)/1)
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