36,495 research outputs found
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
1970, 1925, 2009. Whistling in the stadium as a form of protest
The discovery and documentation of a clandestine handbill dating from the end of Franco's regime calling on supporters to whistle in protest at the dictator at the Camp Nou provides the departure point for a revision of the relation between football as the game of the masses and citizen protest in the case of Catalan political (and sporting) culture of the twentieth and twenty-first centuries. It is based on antecedents and more recent cases of protests at big sporting events, in view of the continuing use of whistling at anthems or government authorities under different political regimes
The cubic polynomial differential systems with two circles as algebraic limit cycles
In this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.The first author is partially supported by a MINECO grant number MTM2014-53703-P, and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The second author is partially supported by a MINECO grant MTM2013-40998-P, an AGAUR grant 2014SGR 568, and two grants FP7-PEOPLE-2012-IRSES numbers 316338 and 318999. The third author is partially supported by FCT/Portugal through the project UID/MAT/04459/2013
Simple inflationary quintessential model II: Power law potentials
The present work is a sequel of our previous work Phys.Rev.D { 93}, 084018
(2016) [arXiv:1601.08175 [gr-qc]] cite{hap} which depicted a simple version of
an inflationary quintessential model whose inflationary stage was described by
a Higgs type potential and the quintessential phase was responsible due to an
exponential potential. Additionally, the model predicted a nonsingular universe
in past which was geodesically past incomplete. Further, it was also found that
the model is in agreement with the Planck 2013 data when running is allowed.
But, this model was found to be unsuccessful with Planck 2015 data with or
without running. However, in this sequel we propose a family of models runs by
a single parameter which proposes another "inflationary
quintessential model" where the inflation and the quintessence regimes are
respectively described by a power law potential and a cosmological constant.
The model is also nonsingular although geodesically past incomplete as in the
cited model. However, the present one is found to be more simple in compared to
the previous model and it is in excellent agreement with the observational
data. We note that unlike the previous model which matched only with Planck
2013 data in presence of running, a large number of the models of this family
with matches with both Planck 2013 and Planck 2015 data
whether the running is allowed or not. Thus, the properties in the current
family of models in compared to its past companion justify its need for a
better cosmological model with the successive improvement of the observational
data.1Comment: Version accepted for publication in PR
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