Periodic motion and the arnold conjecture

Kishore Marathe

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Submission date: 18. Jan. 2000 (revised version: January 2000)
Pages: 23
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Abstract:
We discuss the geometric formulation of the classical Hamiltonian system of equations and the problem of existence of periodic solutions for such systems. After a brief discussion of the Poincaré-Birkhoff theorem we give the most general statement of the Arnold conjecture. In the remaining article we sketch the developments in symplectic topology motivated by the Arnold conjecture culminating in its proof.