Jordan analytic curves which are invariant under rational functions are studied.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-5, author = {Alexandre Eremenko}, title = {Invariant curves and semiconjugacies of rational functions}, journal = {Fundamenta Mathematicae}, volume = {219}, year = {2012}, pages = {263-270}, zbl = {1293.30059}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-5} }
Alexandre Eremenko. Invariant curves and semiconjugacies of rational functions. Fundamenta Mathematicae, Tome 219 (2012) pp. 263-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-5/