166,986 research outputs found
Sietes canciones populares españolas by Manuelde Falla. Arranged for guitar and various instruments by Jaume Torrent.
Sietes canciones populares españolas by Manuel de Falla. Arranged for guitar and various instruments by Jaume Torrent
On the Integrability of Liénard systems with a strong saddle
We study the local analytic integrability for real Li\'{e}nard systems, , with but which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the resonant saddle into a strong saddle.The first author is partially supported by a MINECO/FEDER grant number MTM2014-
53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR-1204. The
second author is partially supported by a FEDER-MINECO grant MTM2016-77278-P, a
MINEC0 grant MTM2013-40998-P, and an AGAUR grant number 2014SGR-568
Viability of the matter bounce scenario in Loop Quantum Cosmology for general potentials
We consider the matter bounce scenario in Loop Quantum Cosmology (LQC) for
physical potentials that at early times provide a nearly matter dominated
Universe in the contracting phase, having a reheating mechanism in the
expanding phase, i.e., being able to release the energy of the scalar field
creating particles that thermalize in order to match with the hot Friedmann
Universe, and finally at late times leading to the current cosmic acceleration.
For these models, numerically solving the dynamical equations we have seen that
the teleparallel version of LQC leads to theoretical results that fit well with
current observational data. More precisely, in teleparallel LQC there is a set
of solutions which leads to theoretical results that match correctly with last
BICEP2 data, and there is another set whose theoretical results fit well with
{\it Planck's} experimental data. On the other hand, in holonomy corrected LQC
the theoretical value of the tensor/scalar ratio is smaller than in
teleparallel LQC, which means that there is always a set of solutions that
matches with {\it Planck's} data, but for some potentials BICEP2 experimental
results disfavours holonomy corrected LQC.Comment: A section about reheating in the matter bounce scenario has been
added. Version accepted for publication in JCA
Boolean Delay Equations: A simple way of looking at complex systems
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with
Boolean-valued variables that evolve in continuous time. Systems of BDEs can be
classified into conservative or dissipative, in a manner that parallels the
classification of ordinary or partial differential equations. Solutions to
certain conservative BDEs exhibit growth of complexity in time. They represent
therewith metaphors for biological evolution or human history. Dissipative BDEs
are structurally stable and exhibit multiple equilibria and limit cycles, as
well as more complex, fractal solution sets, such as Devil's staircases and
``fractal sunbursts``. All known solutions of dissipative BDEs have stationary
variance. BDE systems of this type, both free and forced, have been used as
highly idealized models of climate change on interannual, interdecadal and
paleoclimatic time scales. BDEs are also being used as flexible, highly
efficient models of colliding cascades in earthquake modeling and prediction,
as well as in genetics. In this paper we review the theory of systems of BDEs
and illustrate their applications to climatic and solid earth problems. The
former have used small systems of BDEs, while the latter have used large
networks of BDEs. We moreover introduce BDEs with an infinite number of
variables distributed in space (``partial BDEs``) and discuss connections with
other types of dynamical systems, including cellular automata and Boolean
networks. This research-and-review paper concludes with a set of open
questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular
the discussion on partial BDEs is updated and enlarge
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