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      A C^0 counterexample to the Arnold conjecture

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          Abstract

          The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold must have at least as many fixed points as the minimal number of critical points of a smooth function on the manifold. It is well known that the Arnold conjecture holds for Hamiltonian homeomorphisms of closed symplectic surfaces. The goal of this paper is to provide a counterexample to the Arnold conjecture for Hamiltonian homeomorphisms in dimensions four and higher. More precisely, we prove that every closed and connected symplectic manifold of dimension at least four admits a Hamiltonian homeomorphism with a single fixed point.

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          Author and article information

          Journal
          2016-09-28
          Article
          1609.09192
          c9187b32-692d-4a06-ba68-b37dda82c000

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          53D05, 37C25
          58 pages, 7 figures
          math.SG math.DS

          Differential equations & Dynamical systems,Geometry & Topology
          Differential equations & Dynamical systems, Geometry & Topology

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