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Covers
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Abstract
Every covering dynamical system has a unique image. The same is not true for images. Every image dynamical system has many different inequivalent equivariant covers. We make these statements more precise. Every dynamical system Xi = Fi(X) equivariant under symmetry group ( has a unique image dynamical system u1 = g1(u ). The image is obtained by introducing invariant coordinates u1 = u1(x ). The two dynamical systems are locally diffeomorphic but not globally diffeomorphic. Conversely, a dynamical system u1 = g1(u ) without symmetry can be “lifted” to a covering dynamical system with symmetry group( by introducing a set of coordinates Xi with suitable transformation properties under
Title: Covers
Description:
Abstract
Every covering dynamical system has a unique image.
The same is not true for images.
Every image dynamical system has many different inequivalent equivariant covers.
We make these statements more precise.
Every dynamical system Xi = Fi(X) equivariant under symmetry group ( has a unique image dynamical system u1 = g1(u ).
The image is obtained by introducing invariant coordinates u1 = u1(x ).
The two dynamical systems are locally diffeomorphic but not globally diffeomorphic.
Conversely, a dynamical system u1 = g1(u ) without symmetry can be “lifted” to a covering dynamical system with symmetry group( by introducing a set of coordinates Xi with suitable transformation properties under.
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