2001/06/26 by Leonid Polterovich, Polterovich, Leonid, Jean-Claude Sikorav +1
Computer Science · Mathematics · #(2000) 20F65 (Primary) 53Dxx (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis #math.DS #math.GR #math.SG #msc:20F65 #msc:53Dxx
paper · pdf · doi:10.48550/arxiv.math/0106216
Theorem 1.1 located in published literature, Latex, 14 pages, preliminary version
openalex publication_date 2001/06/26 · arxiv created 2001/06/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It follows from a general theorem of Bonk and Eremenko that closed plane curves which are contractible in the complement to the integral lattice satisfy a linear isoperimetric inequality. We give an alternative proof of this fact. Our approach is based on a non-standard combinatorial isoperimetric inequality which requires a refinement of the small cancellation theory. We present an application of the isoperimetric inequality for the punctured plane to Hamiltonian dynamics. Combining it with methods of symplectic topology we show that every non-identical Hamiltonian diffeomorphism of the 2-torus has at least linear asymptotic growth of the differential.