5,194 research outputs found
Functorial properties of Putnam's homology theory for Smale spaces
We investigate functorial properties of Putnam's homology theory for Smale
spaces. Our analysis shows that the addition of a conjugacy condition is
necessary to ensure functoriality. Several examples are discussed that
elucidate the need for our additional hypotheses. Our second main result is a
natural generalization of Putnam's Pullback Lemma from shifts of finite type to
non-wandering Smale spaces.Comment: Updated to agree with published versio
On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain
A generalization of Jacobi's elliptic functions is introduced as inversions
of hyperelliptic integrals. We discuss the special properties of these
functions, present addition theorems and give a list of indefinite integrals.
As a physical application we show that periodic kink solutions (kink chains) of
the double sine-Gordon model can be described in a canonical form in terms of
generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table
Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type
We discuss a family of multi-term addition formulae for Weierstrass functions
on specialized curves of genus one and two with many automorphisms. In the
genus one case we find new addition formulae for the equianharmonic and
lemniscate cases, and in genus two we find some new addition formulae for a
number of curves, including the Burnside curve.Comment: 19 pages. We have extended the Introduction, corrected some typos and
tidied up some proofs, and inserted extra material on genus 3 curve
Characterizing Planetary Orbits and the Trajectories of Light
Exact analytic expressions for planetary orbits and light trajectories in the
Schwarzschild geometry are presented. A new parameter space is used to
characterize all possible planetary orbits. Different regions in this parameter
space can be associated with different characteristics of the orbits. The
boundaries for these regions are clearly defined. Observational data can be
directly associated with points in the regions. A possible extension of these
considerations with an additional parameter for the case of Kerr geometry is
briefly discussed.Comment: 49 pages total with 11 tables and 10 figure
The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature
The harmonic oscillator as a distinguished dynamical system can be defined
not only on the Euclidean plane but also on the sphere and on the hyperbolic
plane, and more generally on any configuration space with constant curvature
and with a metric of any signature, either Riemannian (definite positive) or
Lorentzian (indefinite). In this paper we study the main properties of these
`curved' harmonic oscillators simultaneously on any such configuration space,
using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii
which altogether correspond to the possible values for curvature and signature
type: the generic Riemannian and Lorentzian spaces of constant curvature
(sphere , hyperbolic plane , AntiDeSitter sphere {\bf
AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this
family, with the Euclidean and Minkowski spaces as flat limits.
We solve the equations of motion for the `curved' harmonic oscillator and
obtain explicit expressions for the orbits by using three different methods:
first by direct integration, second by obtaining the general CK version of the
Binet's equation and third, as a consequence of its superintegrable character.
The orbits are conics with centre at the potential origin in any CK space,
thereby extending this well known Euclidean property to any constant curvature
configuration space. The final part of the article, that has a more geometric
character, presents those results of the theory of conics on spaces of constant
curvature which are pertinent.Comment: 29 pages, 6 figure
Nonlinear feedback oscillations in resonant tunneling through double barriers
We analyze the dynamical evolution of the resonant tunneling of an ensemble
of electrons through a double barrier in the presence of the self-consistent
potential created by the charge accumulation in the well.
The intrinsic nonlinearity of the transmission process is shown to lead to
oscillations of the stored charge and of the transmitted and reflected fluxes.
The dependence on the electrostatic feedback induced by the self-consistent
potential and on the energy width of the incident distribution is discussed.Comment: 10 pages, TeX, 5 Postscript figure
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