Transitive endomorphisms with critical points
نویسندگان
چکیده
منابع مشابه
Fixed points of endomorphisms of graph groups
It is shown, for a given graph group G, that the fixed point subgroup Fix' is finitely generated for every endomorphism ' of G if and only if G is a free product of free abelian groups. The same conditions hold for the subgroup of periodic points. Similar results are obtained for automorphisms if the dependence graph of G is a transitive forest.
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It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. Considering the Foata normal form metric on trace monoids and uniformly continuous endomorphisms, a finiteness theorem is proved for the infinite fixed points of the continuous extension to real traces.
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The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
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It is proved that the periodic point submonoid of a free inverse monoid endomorphism is always finitely generated. Using Chomsky’s hierarchy of languages, we prove that the fixed point submonoid of an endomorphism of a free inverse monoid can be represented by a context-sensitive language but, in general, it cannot be represented by a context-free language.
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This paper investigates the problem of finding the possible sequences of periodic point counts for endomorphisms of solenoids. For an ergodic epimorphism of a solenoid, a closed formula is given which expresses the number of points of any given period in terms of sets of places of finitely many algebraic number fields and distinguished elements of those fields. The result extends to more genera...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13737