A topological degree theory for rotating solutions of planar systems
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 PoincaréBirkhoff Theorem. Some applications to asymptotically linear and superlinear differential equations are discussed.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.04971
 Bibcode:
 2021arXiv210904971G
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Classical Analysis and ODEs;
 37C25 (primary) 34C25;
 37E45;
 37J46 (secondary)