A topological degree theory for rotating solutions of planar systems
arXiv:2109.04971
Abstract
We present a generalized notion of degree for rotating solutions of planar systems. We prove a formula for the relation of such degree with the classical use of Brouwer's degree and obtain a twist theorem for the existence of periodic solutions, which is complementary to the Poincaré-Birkhoff Theorem. Some applications to asymptotically linear and superlinear differential equations are discussed.