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Creators/Authors contains: "Mazzucchelli, Marco"

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  1. ; ; ; (, Selecta Mathematica)
    In this paper we continue investigating connections between Floer theory and dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows. Barcode entropy is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. The key novel result is that the barcode entropy is bounded from below by the topological entropy of any hyperbolic invariant set. This, combined with the fact that the topological entropy bounds the barcode entropy from above, established by Fender, Lee and Sohn, implies that in dimension three the two types of entropy agree. The main new ingredient of the proof is a variant of the Crossing Energy Theorem for Reeb flows. 
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    Free, publicly-accessible full text available September 1, 2026
  2. ; ; (, Journal of the European Mathematical Society)
    We introduce and study the barcode entropy for geodesic flows of closed Riemannian manifolds, which measures the exponential growth rate of the number of not-too-short bars in the Morse-theoretic barcode of the energy functional. We prove that the barcode entropy bounds from below the topological entropy of the geodesic flow and, conversely, bounds from above the topological entropy of any hyperbolic compact invariant set. As a consequence, for Riemannian metrics on surfaces, the barcode entropy is equal to the topological entropy. A key to the proofs and of independent interest is a crossing energy theorem for gradient flow lines of the energy functional. 
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    Free, publicly-accessible full text available December 13, 2025
  3. ; (, Transactions of the American Mathematical Society)
    We consider convex contact spheres Y Y all of whose Reeb orbits are closed. Any such Y Y admits a stratification by the periods of closed Reeb orbits. We show that Y Y “resembles” a contact ellipsoid: any stratum of Y Y is an integral homology sphere, and the sequence of Ekeland-Hofer spectral invariants of Y Y coincides with the full sequence of action values, each one repeated according to its multiplicity. 
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  4. ; (, Commentarii Mathematici Helvetici)
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