Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

Quasi-periodic Gaits in Multi-legged Robots

5th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines

Hyper-IgD and Periodic Fever Syndrome: a New MVK Mutation (p.R277G) Associated with a Severe Phenotype

Hyperimmunoglobulinemia D and periodic fever syndrome (HIDS; MIM#260920) is a rare recessively-inherited autoinflammatory condition caused bymutations in the MVK gene, which encodes for mevalonate kinase, an essential enzyme in the isoprenoid pathway. HIDS is clinically characterized by recurrent episodes of fever and inflammation. Herewe report on the case of a 2 year-old Portuguese boy with recurrent episodes of fever, malaise, massive cervical lymphadenopathy and hepatosplenomegaly since the age of 12 months. Rash, arthralgia, abdominal pain and diarrhea were also seen occasionally. During attacks a vigorous acute-phase response was detected, including elevated erythrocyte sedimentation rate, C-reactive protein, serum amyloid A and leukocytosis. Clinical and laboratory improvement was seen between attacks. Despite normal serum IgD level, HIDS was clinically suspected. Mutational MVK analysis revealed the homozygous genotype with the novel p.Arg277Gly (p.R277G) mutation, while the healthy non consanguineous parents were heterozygous. Short nonsteroidal anti-inflammatory drugs and corticosteroid courses were given during attacks with poor benefits, where as anakinra showed positive responses only at high doses. The p.R277Gmutation here described is a novel missense MVK mutation, and it has been detected in this casewith a severe HIDS phenotype. Further studies are needed to evaluate a co-relation genotype, enzyme activity and phenotype, and to define the best therapeutic strategies.

Design of a power output stage for a class D audio power amplifier based on an 1.5-bit ∑ ∆ M

Dissertação apresentada para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

On the temperature dependence of the absorption cross section for black holes in string theory

We study the low frequency absorption cross section of spherically symmetric nonextremal d-dimensional black holes. In the presence of α′ corrections, this quantity must have an explicit dependence on the Hawking temperature of the form 1/TH. This property of the low frequency absorption cross section is shared by the D1-D5 system from type IIB superstring theory already at the classical level, without α′ corrections. We apply our formula to the simplest example, the classical d-dimensional Reissner-Nordstr¨om solution, checking that the obtained formula for the cross section has a smooth extremal limit. We also apply it for a d-dimensional Tangherlini-like solution with α′3 corrections.

Absorption of scalars by nonextremal charged black holes in string theory

We analyze the low frequency absorption cross section of minimally coupled massless scalar fields by different kinds of charged static black holes in string theory, namely the D1–D5 system in d=5 and a four dimensional dyonic four-charged black hole. In each case we show that this cross section always has the form of some parameter of the solution divided by the black hole Hawking temperature. We also verify in each case that, despite its explicit temperature dependence, such quotient is finite in the extremal limit, giving a well defined cross section. We show that this precise explicit temperature dependence also arises in the same cross section for black holes with string \alpha' corrections: it is actually induced by them.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Periodic orbits in complex Abel equation

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Polynomial and linearized normal forms for almost periodic differential systems

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Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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