FIXED POINTS OF ENDOMORPHISMS OF VIRTUALLY FREE GROUPS

被引:11
作者
Silva, Pedro V. [1 ]
机构
[1] Univ Porto, Ctr Matemat, Fac Ciencias, P-4169007 Oporto, Portugal
关键词
AUTOMORPHISMS; SUBGROUPS;
D O I
10.2140/pjm.2013.263.207
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:207 / 240
页数:34
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