New examples of non-polynomial integrals of two-dimensional geodesic flows *

Abstract

Abstract In this paper, we continue to study integrable geodesic flows on 2-surfaces with non-polynomial first integrals which we started earlier in our previous papers. We construct explicitly new local examples of Riemannian metrics and such integrals via various approaches and methods such as the classical and the generalized hodograph methods, the method of separation of variables and some others.