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Fixed points of
endomorphisms of virtually free groups
Pedro V. Silva |
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Vol. 263 (2013), No. 1, 207–240
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Abstract |
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A fixed point theorem is proved for inverse transducers, which leads to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regular fixed points in the hyperbolic boundary has finitely many orbits under the action of the finite fixed points. In the automorphism case, it is shown that these regular fixed points are either exponentially stable attractors or exponentially stable repellers. |
Keywords
virtually free groups, endomorphisms, fixed points,
hyperbolic boundary, classification of fixed points
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Mathematical Subject Classification 2010
Primary: 20E05, 20E36, 20F67
Secondary: 68Q45, 37B25
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Milestones
Received: 12 April 2012
Revised: 7 November 2012
Accepted: 19 November 2012
Published: 14 May 2013
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Authors |
| Pedro V. Silva | |
| Centro de Matemática, Faculdade de
Ciências Universidade do Porto R. Campo Alegre 687 4169-007 Porto Portugal |
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