Reversibility properties of semigroup actions on homogeneous spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

Continuously deformable topological structure

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Disclosing the generic behavior of topological solutions: An orbit-based approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonpolynomial potentials with deformable topological structures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Topological K-equivalence of analytic function-germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finiteness theorem for topological contact equivalence of map germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Integrable hierarchy for multidimensional Toda equations and topological-anti-topological fusion

The negative symmetry flows are incorporated into the Riemann-Hilbert problem for the homogeneous A(m)-hierarchy and its (gl) over cap (m + 1, C) extension.A loop group automorphism of order two is used to define a sub-hierarchy of (gl) over cap (m + 1, C) hierarchy containing only the odd symmetry flows. The positive and negative flows of the +/-1 grade coincide with equations of the multidimensional Toda model and of topological-anti-topological fusion. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Quadratic gravity in (2+1)D with a topological Chern-Simons term

Three-dimensional quadratic gravity, unlike general relativity in (2+1)D, is dynamically nontrivial and has a well behaved nonrelativistic potential. Here we analyse the changes that occur when a topological Chem-Simons term is added to this theory. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin 2. We also found that light deflection does not have the 'wrong sign' such as in the framework of three-dimensional quadratic gravity.

Can one cure the nommitarity of three-dimensional quadratic gravity using a topological Chern-Simons term?

Quadratic gravity in (2+1)D is nonunitarity at the tree level. When a topological Chern-Simons term is added to this theory, the harmless massive scalar mode of the former gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin-2. Therefore, unlike what it is claimed in the literature, quadratic Chern-Simons gravity in (2+1)D is nonunitary at the tree level.

A model for Hopfions on the space-time S(3)xR

We construct static and time dependent exact soliton solutions for a theory of scalar fields taking values on a wide class of two dimensional target spaces, and defined on the four dimensional space-time S-3 X R. The construction is based on an ansatz built out of special coordinates on S3. The requirement for finite energy introduce boundary conditions that determine an infinite discrete spectrum of frequencies for the oscillating solutions. For the case where the target space is the sphere S-2, we obtain static soliton solutions with nontrivial Hopf topological charges. In addition, such Hopfions can oscillate in time, preserving their topological Hopf charge, with any of the frequencies belonging to that infinite discrete spectrum. (C) 2005 American Institute of Physics.

Quasiprobability distribution functions for periodic phase spaces: I. Theoretical aspects

An approach featuring s-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach, a suitable set of angle - angular momentum coherent states must be constructed in an appropriate fashion.

Noether and topological currents equivalence and soliton/particle correspondence in affine sl(2)((1)) Toda theory coupled to matter

A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivalence between the Noether and topological currents. The classical solitonic spectrum of the ATM model is also discussed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Schwinger and Pegg-Barnett approaches and a relationship between angular and Cartesian quantum descriptions: II. Phase spaces

Following the discussion-in state-space language-presented in a preceding paper, we work on the passage from the phase-space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labelled) number of states. With this it is possible to relate an original Schwinger idea to the Pegg-Barnett approach to the phase problem. In phase-space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase-space formalism.