Showing papers on "Winding number published in 1984"
TL;DR: In this paper, it was shown that a forced oscillation problem for a Hamiltonian equation on a torus possesses a periodic solution having minimal period T, for every sufficiently large prime number T. The proof uses the classical variational approach.
Abstract: : A forced oscillation problem for a Hamiltonian equation on a torus is studied, If the dimension of the torus is equal to 2n, and if the period of the time dependent Hamiltonian equation is equal to 1, there are at least (2n+1) periodic solutions having period 1. In this paper it is shown, that, under an additional, necessary nondegeneracy condition such an equation possesses a periodic solution having minimal period T, for every sufficiently large prime number T. The proof uses the classical variational approach. It is based on the Morse theory for periodic solution to its Morse index and on an iteration formula for the winding number. Originator-supplied keywords included: Hamiltonian systems, Periodic solutions, Variational principles, Morse-type index theory, Winding number of a periodic solution, and Reprints.
28 citations
TL;DR: In this article, the authors considered the problem of the disposition of the set of points of a nonsingular real algebraic curve of given degree in ℂP2 and proved that the complement indicated is homotopy equivalent with a 3D cell complex of special form.
Abstract: In this paper we consider the problem of the disposition of the set of points of a nonsingular real algebraic curve of given degree in ℂP2. The homotopy description of the complement of such a curve in ℂP2 is the first step toward solving the problem of disposition mentioned. In the case of an arbitrary curve we are able to prove that the complement indicated is homotopy equivalent with a three-dimensional cell complex of special form. For a certain class of curves the complex turns out to be two-dimensional and admits a precise description, which allows us to calculate its fundamental group. The results are given without proof.
9 citations
TL;DR: In this article, the Coulomb interactions generated by the complete abelian subgroup of the unbroken gauge group were analyzed for general spherically symmetric monopoles of arbitrary strength and massless fermions in arbitrary representations of the gauge group.
6 citations
TL;DR: In this article, the classical perturbation series is used to follow an invariant curve, of fixed winding number, up to its break-up point, and the result obtained for the critical value of the perturbations and the corresponding behaviour of the invariant curves are in complete agreement with the results of Kadanoff and Shenker.
3 citations
TL;DR: In this article, a plausible conjecture regarding the source of universality is proposed, and the nature of the singularity at the critical point and the asymptotic character of the continued fraction representation of the winding number determine the universality class.
3 citations
1 citations
TL;DR: In this paper, finite-energy configurations in SO(N) gauge theories with Higgs fields in the fundamental representation are studied, and the corresponding energy density is spherically symmetric.
Abstract: We study finite-energy configurations in SO(N) gauge theories with Higgs fields in the fundamental representation. For all winding numbers, noncontractible hyperloops are constructed. The corresponding energy density is spherically symmetric, and the configuration with maximal energy on each hyperloop can be determined. Noncontractible hyperloops with an arbitrary winding number for SU(2) gauge theory are also given.
1 citations
TL;DR: In this paper, the dynamics of the circle map is studied in the supercritical regime, where the trajectory elements are clustered on the circle and the existence of a simple ordering structure is established for trajectories with arbitrary irrational winding number.
Abstract: The dynamics of the circle map is studied in the supercritical regime where the map is not invertible and thus the trajectory elements are clustered on the circle. Existence of a simple ordering structure is established for trajectories with arbitrary irrational winding number. A previously developed formalism is then generalized to predict the trajectories when the winding number is quadratically irrational. Explicit results are given for a simple case.