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A topological degree theory for rotating solutions of planar systems (2109.04971v2)
Published 10 Sep 2021 in math.DS and math.CA
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 Poincar\'e-Birkhoff Theorem. Some applications to asymptotically linear and superlinear differential equations are discussed.
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