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GEOMETRIC PHASES IN DISSIPATIVE SYSTEMS WITH SYMMETRY
 

Summary: GEOMETRIC PHASES IN DISSIPATIVE
SYSTEMS WITH SYMMETRY
Sean B. Andersson 1
Division of Engineering and Applied Sciences
Harvard University, Cambridge, MA 02318
Abstract: Classical dissipative systems with symmetry can exhibit a geometric
phase effect wherein an adiabatic variation of a parameter drives a shift in the
symmetry direction. Viewing the parameter as a control variable, the effect may
be useful in the parametric control of dissipative systems, many of which exhibit
pattern-forming solutions. Earlier work by A.S. Landsberg developed a theory for
this effect in systems admitting an abelian symmetry. In this paper we present a
generalization allowing for arbitrary continuous symmetries. This generalization
is achieved by defining a new principal connection, here called the Landsberg
connection, on an appropriate principal fiber bundle. A simple example is presented
to illustrate the theory.
Keywords: nonlinear systems, phase shift, perturbation analysis, dissipation,
geometric approaches
1. INTRODUCTION
Dissipation is a common feature in physical sys-
tems and can give rise to interesting dynamics

  

Source: Andersson, Sean B. - Department of Aerospace and Mechanical Engineering, Boston University

 

Collections: Engineering