What is it about?

We give a normal form for group actions on manifolds endowed with symplectic structures with mild singularities (called b-symplectic/log-symplectic manifolds). These normal forms give an accurate description of the geometric structure in a neighborhood of the orbit of the group actions.

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Why is it important?

b-Symplectic structures appear naturally on symplectic manifolds with boundary and on several physical problems including the 3-body problem. Thus understanding these structures can have important applications in Physical systems when symmetries are considered.


I hope this article is helpful to find new applications in Physics and in the study of Symplectic and Hamiltonian Dynamics with singularities.

Eva Miranda
Universitat Politecnica de Catalunya

Read the Original

This page is a summary of: A b$b$‐symplectic slice theorem, Bulletin of the London Mathematical Society, August 2022, Wiley,
DOI: 10.1112/blms.12713.
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