Corpus ID: 237571401

# On GIT quotients of the symplectic group, stability and bifurcations of symmetric orbits

@inproceedings{Frauenfelder2021OnGQ,
title={On GIT quotients of the symplectic group, stability and bifurcations of symmetric orbits},
author={Urs Frauenfelder and Agust{\'i}n Moreno},
year={2021}
}
• Published 19 September 2021
• Mathematics, Physics
We provide topological obstructions to the existence of orbit cylinders of symmetric orbits, for mechanical systems preserved by antisymplectic involutions (e.g. the restricted three-body problem). Such cylinders induce continuous paths which do not cross the bifurcation locus of suitable GIT quotients of the symplectic group, which are branched manifolds whose topology provide the desired obstructions. Namely, the complement of the corresponding loci consist of several connected components… Expand

#### References

SHOWING 1-10 OF 21 REFERENCES
Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem
The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine verticalExpand
The space of linear anti-symplectic involutions is a homogenous space
• Mathematics
• 2012
In this note we prove that the space of linear anti-symplectic involutions is the homogenous space $${{{\rm Gl}(n, \mathbb{R})\backslash{\rm Sp}(n)}}$$ . This result is motivated by the study ofExpand
The Hörmander index of symmetric periodic orbits
• Mathematics
• 2012
A symmetric periodic orbit is a special kind of periodic orbit that can also be regarded as a Lagrangian intersection point. Therefore it has two Maslov indices whose difference is the HörmanderExpand
Convexity Methods In Hamiltonian Mechanics
I. Linear Hamiltonian Systems.- 1. Floquet Theory and Stability.- 2. Krein Theory and Strong Stability.- 3. Time-Dependence of the Eigenvalues of R (t).- 4. Index Theory for Positive DefiniteExpand
Index Theory for Symplectic Paths with Applications
I The Symplectic Group Sp(2n).- 1 Algebraic Aspects.- 1.1 Symplectic matrices.- 1.2 Symplectic spaces.- 1.3 Eigenvalues of symplectic matrices.- 1.4 Normal forms for the eigenvalue 1.- 1.5 NormalExpand
Iteration Formulae for Brake Orbit and Index Inequalities for Real Pseudoholomorphic Curves
I give precise iteration formulae for brake orbit in dimension 3 and use these formulae to get some index inequalities for moduli spaces of Real pseudoholomorphic Curves, which are important toExpand
On the theory of entire matrix-functions of exponential type
It is shown that if an entire matrix function U(λ) is J inner, then it is of exponential type and (1+λ2)-1ln +||U(λ)|| is summable. These results are applied to the monodromy matrix of a canonicalExpand
A Morse Theory for Hamiltonian Systems
Publisher Summary This chapter discusses the Morse theory for Hamiltonian systems. The chapter presents the differential equation. The chapter presents infinite dimensional case Bott's Morse theoryExpand