2013/05/31 by Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini · 1 citation
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Hamiltonian (control theory) #Hamiltonian system #Mathematical Dynamics and Fractals #Property (philosophy) #Quantum chaos and dynamical systems #Rigidity (electromagnetism) #Symplectic geometry #Uniqueness #math.SG
paper · pdf · doi:10.1215/00127094-2881701
published as Duke Math. J. 164, no. 4 (2015), 767-799 · 27 pages. v2. Significant reorganization of the paper, several typos and inaccuracies corrected after the refeering process. A theorem (Theorem 5, completing the study of C^0 dynamical properties of coisotropics) added. To appear in Duke Mathematical Journal
arxiv created 2015/02/03 · openalex publication_date 2015/03/15 · arxiv updated 2015/11/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We prove that symplectic homeomorphisms, in the sense of the celebrated Gromov–Eliashberg Theorem, preserve coisotropic submanifolds and their characteristic foliations. This result generalizes the Gromov–Eliashberg theorem and demonstrates that previous rigidity results (on Lagrangians by Laudenbach and Sikorav, and on characteristics of hypersurfaces by Opshtein) are manifestations of a single rigidity phenomenon. To prove the above, we establish a C0-dynamical property of coisotropic submanifolds which generalizes a foundational theorem in C0-Hamiltonian dynamics: uniqueness of generators for continuous analogues of Hamiltonian flows.