Marco MazzucchelliENG
 ˇ  FR

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My research is in dynamical systems, Riemannian geometry, and symplectic topology. In particular I am interested in the study of periodic orbits of Hamiltonian systems in several settings, including the problem of closed geodesics in Riemannian or Finsler manifolds, periodic trajectories in billiards, and periodic points of Hamiltonian diffeomorphisms. As an undergraduate, I also worked on the algebraic theory of inverse semigroups.

Preprints
  • (with Gabriele Benedetti) Infinitely many periodic orbits just above the Mańé critical value on the 2-sphere
    preprint: pdf

Papers
  • (with Luca Asselle) On Tonelli periodic orbits with low energy on surfaces
    to appear in Transactions of the American Mathematical Society
    preprint: pdf,    published version: pdf

  • (with Leonardo Macarini) Isometry-invariant geodesics and the fundamental group, II
    Advances in Mathematics 308 (2017), 671-698
    preprint: pdf,    published version: pdf

  • (with A. Abbondandolo, L. Asselle, G. Benedetti, I. A. Taimanov) The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere
    Advanced Nonlinear Studies 17 (2017), no. 1, 17-30
    preprint: pdf,    published version: pdf

  • (with Colin Guillarmou) Marked boundary rigidity for surfaces
    to appear in Ergodic Theory and Dynamical Systems
    preprint: pdf
    ,    published version: pdf

  • (with Luca Asselle) On the existence of infinitely many closed geodesics on non-compact manifolds
    Proceedings of the American Mathematical Society 145 (2017), no. 6, 2689-2697
    preprint: pdf
    ,    published version: pdf

  • (with A. Abbondandolo, L. Macarini, and G. P. Paternain) Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level
    Journal of the European Mathematical Society 19 (2017), no. 2, 551-579
    preprint: pdf
    ,    published version: pdf

  • The Morse index of Chaperon's generating families
    Publicaciones Matemáticas del Uruguay 16 (2016), 81-125
    preprint: pdf
    ,    published version: pdf

  • (with Alfonso Sorrentino) Remarks on the symplectic invariance of Aubry-Mather sets
    Comptes Rendus de l'Académie des Sciences de Paris -
    Séries I 354 (2016), no. 4, 419-423
    preprint: pdf
    ,    published version: pdf

  • Isometry-invariant geodesics and the fundamental group
    Mathematische Annalen 362 (2015), no. 1-2, 265-280

    preprint: pdf,    published version: pdf

  • On the multiplicity of isometry-invariant geodesics on product manifolds
    Algebraic & Geometric Topology 14 (2014), 135-156
    preprint: pdf
    ,    published version: pdf

  • Symplectically degenerate maxima via generating functions
    Mathematische Zeitschrift 275 (2013), no. 3-4, 715-739
    preprint
    : pdf,    published version: pdf

  • On the multiplicity of non-iterated periodic billiard trajectories
    Pacific Journal of Mathematics 252 (2011), no. 1, 181-205
    preprint
    : pdf,    published version: pdf

  • (with Peter Albers) Periodic bounce orbits of prescribed energy
    International Mathematics Research Notices 2011, no. 14, 3289-3314
    preprint: pdf
    ,    published version: pdf

  • The Lagrangian Conley conjecture
    Commentarii Mathematici Helvetici 86 (2011), no. 1, 189-246
    preprint: pdf
    ,    published version: pdf

  • (with Alessandra Cherubini) On the Decidability of the Word Problem for Amalgamated Free Products of Inverse Semigroups
    Semigroup Forum 76 (2008), no. 2, 309-329
    preprint: pdf,    published version: pdf

Books
  • Critical point theory for Lagrangian systems
    Progress in Mathematics, vol. 293, Birkhäuser
    publisher webpage
    errata corrige: pdf

Theses
  • Periodic orbits of Tonelli Lagrangian systems
    Ph.D. Thesis, Universitŕ di Pisa
    advisor: Alberto Abbondandolo

  • Applicazioni della teoria degli automi al problema della parola in semigruppi inversi
    Master Thesis, Politecnico di Milano
    advisor: Alessandra Cherubini