237 research outputs found
Closed orbits of a charge in a weakly exact magnetic field
We prove that for a weakly exact magnetic system on a closed connected
Riemannian manifold, almost all energy levels contain a closed orbit. More
precisely, we prove the following stronger statements. Let denote a
closed connected Riemannian manifold and a weakly exact 2-form. Let
denote the magnetic flow determined by , and let denote
the Mane critical value of the pair . We prove that if , then
for every non-trivial free homotopy class of loops on there exists a closed
orbit with energy whose projection to belongs to that free homotopy
class. We also prove that for almost all there exists a closed orbit with
energy whose projection to is contractible. In particular, when
this implies that almost every energy level has a contractible
closed orbit. As a corollary we deduce that if is not exact and
has an amenable fundamental group (which implies ) then there exist
contractible closed orbits on almost every energy level.Comment: 25 pages. v3 - minor corrections, this version to appear in PJ
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
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
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
Paysans, bergers et colporteurs: La vie d'un village de l'âge du Fer dans la Péninsule de Oman (AM1-Thuqeibah, Sharjah, E.A.U.)
Les fouilles archéologiques menées en al Madam (Sharjah, Emirats Arabes Unis) répondent à diverses questions
restées en suspens relatives à l’histoire et l’archéologie del’âge du Fer dans la Péninsule d’Oman. L’ètroite
collaboration entre l’histoire, l’archéologie et les sciences naturelles peutre trouver les modes de vie et l’histoire
quotidienne d’une petite communauté rurale. Il a même aidé à découvrir des facettes imprévuesArchaeological excavations carried out in the al Madam oasis (Sharjah, UAE) are responding to various
questions related to the history and archaeology of the Iron Age in the Oman Peninsula. Close cooperation
between history, archaeology and natural sciences can recover the way of life and every day story of a small
rural community, even discovering unexpected facets
Nueva España en el siglo XVIII
Trabajo sobre las jurisdicciones de la Nueva España y el sistema de intendencia
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)
Topological entropy and blocking cost for geodesics in riemannian manifolds
For a pair of points in a compact, riemannian manifold let
(resp. ) be the number of geodesic segments with length
joining these points (resp. the minimal number of point obstacles
needed to block them). We study relationships between the growth rates of
and as . We derive lower bounds on
in terms of the topological entropy and its fundamental group. This
strengthens the results of Burns-Gutkin \cite{BG06} and Lafont-Schmidt
\cite{LS}. For instance, by \cite{BG06,LS}, implies that is
unbounded; we show that grows exponentially, with the rate at least
.Comment: 13 page
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
- …