Fixed Points of Maps on the Space of Rational Functions

Details Fixed Points of Maps on the Space of Rational Functions Fixed Points of Maps on the Space of Rational Functions

2004-12-17

arxiv.org/abs/math/0412355v1

Mathematics

Classical Analysis and ODEs

7 pages

Scientific paper

Given integers s,t, define a function phi_{s,t} on the space of all formal series expansions by phi_{s,t} (sum a_n x^n) = sum a_{sn+t} x^n. For each function phi_{s,t}, we determine the collection of all rational functions whose Taylor expansions at zero are fixed by phi_{s,t}. This collection can be described as a subspace of rational functions whose basis elements correspond to certain s-cyclotomic cosets associated with the pair (s,t).

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