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On the Maslov index in a symplectic reduction and applications


Author: Henrique Vitório
Journal: Proc. Amer. Math. Soc. 148 (2020), 3517-3526
MSC (2010): Primary 53D12
DOI: https://doi.org/10.1090/proc/14985
Published electronically: March 4, 2020
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Abstract: We provide a short and self-contained proof of an equality of Maslov indices in a linear symplectic reduction and apply it to obtain an equality of Maslov focal indices after reducing by symmetries an electromagnetic Lagrangian system.


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Additional Information

Henrique Vitório
Affiliation: Departamento de Matemática, Universidade Federal de Pernambuco, Cidade Universitária, Recife, Pernambuco, Brazil
Email: henriquevitorio@dmat.ufpe.br

DOI: https://doi.org/10.1090/proc/14985
Keywords: Maslov index, symplectic reduction, focal points, electromagnetic Lagrangian systems
Received by editor(s): September 16, 2019
Received by editor(s) in revised form: November 25, 2019, and December 11, 2019
Published electronically: March 4, 2020
Additional Notes: This work was supported by CNPq, grant No. 232664/2014-5 and the Brazilian program Science Without Borders, grant No. 232664/2014-5.
Dedicated: Dedicated to Professor Fernando F. Cardoso on the occasion of his 80th birthday
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2020 American Mathematical Society