On a product formula for the Conley–Zehnder index of symplectic paths and its applications |
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| Authors: | Maurice De Gosson Serge De Gosson Paolo Piccione |
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| Institution: | 1. Departamento De Matemática, Instituto De Matemática E Estatística, Universidade de S?o Paulo, Rua Do Mat?o 1010, CEP 05508-090, Sao Paulo, SP, Brazil
2. Max-Planck-Institut für Mathematik Pf. 7280, DE-53072, Bonn, Germany
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| Abstract: | Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product
formula for the Conley–Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two
applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.
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| Keywords: | Conley– Zehnder index |
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