0000000000139755
AUTHOR
P. Vindel
Round-handle decomposition ofS2×S1
A round-handle decomposition is associated with a non-singular Morse–Smale flow on 3-manifolds prime to S 2× S 1. This decomposition has been built only for the 3-sphere S 3. In this paper we obtain the round-handle decomposition of non-singular Morse–Smale flows on S 2× S 1, in order to get all the different fattened round handles in this manifold. Some of them include non-separating boundary components that induce the topology of the links of periodic orbits.
Links and Bifurcations in Nonsingular Morse–Smale Systems
Wada's theorem classifies the set of periodic orbits in NMS systems on S3 as links, that can be written in terms of six operations. This characterization allows us to study the topological restrictions that links require to suffer a given codimension one bifurcation. Moreover, these results are reproduced in the case of NMS systems with rotational symmetries, introducing new geometrical tools.
Bifurcations of Links of Periodic Orbits in Non-Singular Systems with Two Rotational Symmetries on S3
A topological characterization of all possible links composed of the periodic orbits of a Non Singular Morse-Smale flow on S3 has been made by M. Wada. The presence of symmetry forces the appearance of given types of links. In this paper we introduce a geometrical tool to represent these type of links when a symmetry around two axes is considered on NMS systems: mosaics. On the other hand, we use mosaics to study what kind of bifurcation can occur in this type of system maintaining the symmetry.
Orbital Structure of the Two Fixed Centres Problem
The set of orbits of the Two Fixed Centres problem has been known for a long time (Charlier, 1902, 1907; Pars, 1965), since it is an integrable Hamiltonian system.
Bifurcations of links of periodic orbits in non-singular Morse–Smale systems with a rotational symmetry on S3
Abstract In this paper we consider a rotational symmetry on a non-singular Morse–Smale (NMS) system analyzing the restrictions this symmetry imposes on the links defined by the set of its periodic orbits and to the appearance of local generic codimension one bifurcations in the set of NMS flows on S 3 . The topological characterization is obtained by writing the involved links in terms of Wada operations. It is also obtained that symmetry implies that in general bifurcations have to be multiple. On the other hand, we also see that there exists a set of links that cannot be related to any other by sequences of this kind of bifurcation.
Superfield commutators for D = 4 chiral multiplets and their apppications
The superfield commutators and their corresponding equal-time limits are derived in a covariant way for the D=4 free massive chiral multiplet. For interesting chiral multiplets, the general KAllen-Lehmann representation is also introduced. As applications of the free superfield commutators, the general solution of the Cauchy problem for chiral superfields is given, and an analysis of the closure of the bilinear products of superfields which desrcibe the extension of the internal currents for free supersymmetric chiral matter is performed.
Bifurcations of links of periodic orbits in non-singular Morse - Smale systems on
The set of periodic orbits of a non-singular Morse - Smale (NMS) flow on defines a link; a characterization of all possible links of NMS flows on has been developed by Wada. In the frame of codimension-one bifurcations, this characterization allows us to study the restrictions a link requires for suffering a given bifurcation. We also derive the topological description of the new link and the possibility of relating links by a chain of this type of bifurcation.
SUPERFIELDS AND CANONICAL METHODS IN SUPERSPACE
We consider the “supersymmetric roots” of the Heisenberg evolution equation as describing the dynamics of superfields in superspace. We investigate the superfield commutators and their equal time limits and exhibit their noncanonical character even for free superfields. For simplicity, we concentrate on the D=1 case, i.e., the superfield formulation of supersymmetric quantum mechanics in the Heisenberg picture and, as a soluble example, the supersymmetric oscillator. Finally, we express Noether’s theorem in superspace and give the definition of the global conserved supercharges.