arXiv Analytics

Sign in

arXiv:math/9606217 [math.DS]AbstractReferencesReviewsResources

On the functional equation f(p(z))=g(q(z)), where p,q are "generalized" polynomials and f,g are meromorphic functions

Sergei Lysenko

Published 1996-06-13Version 1

The functional equation f(p(z))=g(q(z)) is studied, where p,q are polynomials and f,g are trancendental meromorphic functions in C. We find all the pairs p,q for which there exist nonconstant f,g satisfying our equation and there exist no rational f,g with this property. In fact, a more general problem is solved. In addition to algebraic methods, some results from local analytic dynamics are used.

Categories: math.DS
Related articles: Most relevant | Search more
arXiv:0712.0963 [math.DS] (Published 2007-12-06)
A p-adic approach to local analytic dynamics: analytic flows and analytic maps tangent to the identity
arXiv:1312.7554 [math.DS] (Published 2013-12-29, updated 2015-04-24)
Equidistribution towards the bifurcation current I : Multipliers and degree d polynomials
arXiv:2103.10835 [math.DS] (Published 2021-03-19)
Topological mild mixing of all orders along polynomials

Links

Toolbox