Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

Closed string thermal torus from thermo field dynamics

In this Letter a topological interpretation for the string thermal vacuum in the thermo field dynamics (TFD) approach is given. As a consequence, the relationship between the imaginary time and TFD formalisms is achieved when both are used to study closed strings at finite temperature. The TFD approach starts by duplicating the system's degrees of freedom, defining an auxiliary (tilde) string. In order to lead the system to finite temperature a Bogoliubov transformation is implemented. We show that the effect of this transformation is to glue together the string and the tilde string to obtain a torus. The thermal vacuum appears as the boundary state for this identification. Also, from the thermal state condition, a Kubo-Martin-Schwinger condition for the torus topology is derived. © 2005 Elsevier B.V. All rights reserved.

Effect of robust torus on the dynamical transport

In the present work, we quantify the fraction of trajectories that reach a specific region of the phase space when we vary a control parameter using two symplectic maps: one non-twist and another one twist. The two maps were studied with and without a robust torus. We compare the obtained patterns and we identify the effect of the robust torus on the dynamical transport. We show that the effect of meandering-like barriers loses importance in blocking the radial transport when the robust torus is present.

Free actions of abelian p-groups on the n-torus

In this work we make some contributions to the theory of actions of abelian p-groups on the n-Torus T-n. Set congruent to Z(pk1)(h1) x Z(pk2)(h2) x...x Z(pkr)(hr), r >= 1, k(1) >= k(2) >=...>= k(r) >= 1, p prime. Suppose that the group H acts freely on T-n and the induced representation on pi(1)(T-n) congruent to Z(n) is faithful and has first Betti number b. We show that the numbers n, p, b, k(i) and h(i) (i = 1,..,r) satisfy some relation. In particular, when H congruent to Z(p)(h), the minimum value of n is phi(p) + b when b >= 1. Also when H congruent to Z(pk1) x Z(p) the minimum value of n is phi(p(k1)) + p - 1 + b for b >= 1. Here phi denotes the Euler function.

Fixed points on torus fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.

Morphology and incidence of torus palatinus and mandibularis in Brazilian Indians

The incidence and morphology of torus platinus and mandibularis was verified in 200 Indians, residents of two Brazilian Indian Reserves in Sao Paulo State, Brazil. A low incidence of both types of exostoses was observed, with torus palatinus occurring more frequently than mandibularis. These structures did not occur in individuals less than 10 years of age. Flattened torus palatinus predominated in relation to the other forms.

The Noether theorem for geometric actions and area preserving diffeomorphisms on the torus

We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. © 2010 Elsevier B.V. All rights reserved.

On singular foliations on the solid torus

We study smooth foliations on the solid torus S1×D2 having S1×{0} and S1×∂D2 as the only compact leaves and S1×{0} as singular set. We show that all other leaves can only be cylinders or planes, and give necessary conditions for the foliation to be a suspension of a diffeomorphism of the disc. © 2013 Elsevier B.V.

A note on pairs of regular foliations on the solid torus

We discuss the geometry of the pair of foliations on a solid torus given by the Reeb foliation together with discs transverse to the boundary of the torus.

A survey on the set of periods of the graph homeomorphisms

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Structure of 2-keto-3-deoxy-6-phosphogluconate (KDPG) aldolase from Pseudomonas putida

2-Keto-3-deoxy-6-phosphogluconate (KDPG) aldolase from Pseudomonas putida is a key enzyme in the Entner-Doudoroff pathway which catalyses the cleavage of KDPG via a class I Schiff-base mechanism. The crystal structure of this enzyme has been refined to a crystallographic residual R = 17.1% (R-free = 21.4%). The N-terminal helix caps one side of the torus of the (betaalpha)(8)-barrel and the active site is located on the opposite, carboxylic side of the barrel. The Schiff-base-forming Lys145 is coordinated by a sulfate (or phosphate) ion and two solvent water molecules. The interactions that stabilize the trimer are predominantly hydrophobic, with the exception of the cyclically permuted bonds formed between Glu132 OE1 of one molecule and Thr129 OG1 of a symmetry-equivalent molecule. Except for the N-terminal helix, the structure of KDPG aldolase from P. putida closely resembles the structure of the homologous enzyme from Escherichia coli.