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.
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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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