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| Affinely Prime Dynamical Systems |
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Citation： |
Hillel FURSTENBERG,Eli GLASNER,Benjamin WEISS.Affinely Prime Dynamical Systems[J].Chinese Annals of Mathematics B,2017,38(2):413~424 |
| Page view： 613
Net amount： 612 |
Authors： |
Hillel FURSTENBERG; Eli GLASNER;Benjamin WEISS |
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| Abstract： |
This paper deals with representations of groups by ``affine"
automorphisms of compact, convex spaces, with special focus on
``irreducible" representations: equivalently ``minimal" actions.
When the group in question is $PSL(2,\R)$, the authors exhibit a
one-one correspondence between bounded harmonic functions on the
upper half-plane and a certain class of irreducible representations.
This analysis shows that, surprisingly, all these representations
are equivalent. In fact, it is found that all irreducible affine
representations of this group are equivalent. The key to this is a
property called ``linear Stone-Weierstrass" for group actions on
compact spaces. If it holds for the ``universal strongly proximal
space" of the group (to be defined), then the induced action on the
space of probability measures on this space is the unique
irreducible affine representation of the group. |
Keywords： |
Irreducible affine dynamical systems, Affinely prime, Strongproximality, M"{o}bius transformations, Harmonic functions |
Classification： |
31A05, 37B05, 54H11, 54H20 |
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