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We present a topological approach to the problem of the existence of unstable periodic solutions for 2-dimensional, time-periodic ordinary differential equations. This approach makes use of the braid invariant, which is one of the topological invariants for periodic solutions exploiting a concept in the low-dimensional topology. Using the braid invariant, an equivalence relation on the set of periodic solutions is defined. We prove that any equivalence class consisting of at least two solutionsdoi:10.12775/tmna.1999.033 fatcat:mqtk7cdheja37oyugelzr4cfwm