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Bifurcations of periodic orbits are a fundamental phenomenon in Hamiltonian dynamics, and their generic types in 4-dimensional systems are classified through Meyer's work. From the Floer-theoretic viewpoint, a bifurcation changes the generators of the local Floer complex and may also change their Conley–Zehnder indices. While the resulting local Floer homology remains invariant under suitable perturbations, the corresponding chain-level change has not been systematically understood. In the joint work with Hong-Kwon Jo, we investigate how local Floer chain complexes change across generic Hamiltonian bifurcations. We construct localized model Hamiltonians and use them to describe explicit Floer cylinders near the bifurcating orbits, which we call gradient revolutions. This leads to a concrete computation of the induced changes in the local Floer differential, giving a chain-level perspective on the interaction between bifurcation theory and Floer theory.
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