212 research outputs found
Automorphic measures and invariant distributions for circle dynamics
Let be a circle diffeomorphism with irrational rotation
number. As established by Douady and Yoccoz in the eighties, for any given
there exists a unique automorphic measure of exponent for . In the
present paper we prove that the same holds for multicritical circle maps, and
we provide two applications of this result. The first one, is to prove that the
space of invariant distributions of order 1 of any given multicritical circle
map is one-dimensional, spanned by the unique invariant measure. The second
one, is an improvement over the Denjoy-Koksma inequality for multicritical
circle maps and absolutely continuous observables.Comment: 33 pages, 3 figures. Comments are welcom
Dirac physical measures on saddle-type fixed points
In this article we study some statistical aspects of surface diffeomorphisms.
We first show that for a generic diffeomorphism, a Dirac invariant
measure whose \emph{statistical basin of attraction} is dense in some open set
and has positive Lebesgue measure, must be supported in the orbit of a sink. We
then construct an example of a -diffeomorphism having a Dirac invariant
measure, supported on a hyperbolic fixed point of saddle type, whose
statistical basin of attraction is a nowhere dense set with positive Lebesgue
measure. Our technique can be applied also to construct a diffeomorphism
whose set of points with historic behaviour has positive measure and is nowhere
dense.Comment: 63 pages, 26 figures. Final version, accepted in Journal of Dynamics
and Differential Equation
Measurement of the cosmic ray spectrum above eV using inclined events detected with the Pierre Auger Observatory
A measurement of the cosmic-ray spectrum for energies exceeding
eV is presented, which is based on the analysis of showers
with zenith angles greater than detected with the Pierre Auger
Observatory between 1 January 2004 and 31 December 2013. The measured spectrum
confirms a flux suppression at the highest energies. Above
eV, the "ankle", the flux can be described by a power law with
index followed by
a smooth suppression region. For the energy () at which the
spectral flux has fallen to one-half of its extrapolated value in the absence
of suppression, we find
eV.Comment: Replaced with published version. Added journal reference and DO
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