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Linear instability for periodic orbits of non-autonomous Lagrangian systems
- Source :
- Nonlinearity. 34:237-272
- Publication Year :
- 2021
- Publisher :
- IOP Publishing, 2021.
-
Abstract
- Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic solutions of a non-autonomous Lagrangian on a finite dimensional Riemannian manifold. We establish a general criterion for a priori detecting the linear instability of a periodic orbit on a Riemannian manifold for a (maybe not Legendre convex) non-autonomous Lagrangian simply by looking at the parity of the spectral index, which is the right substitute of the Morse index in the framework of strongly indefinite variational problems and defined in terms of the spectral flow of a path of Fredholm quadratic forms on a Hilbert bundle.<br />Comment: 32 pages, no figures
- Subjects :
- Path (topology)
Geodesic
FOS: Physical sciences
General Physics and Astronomy
Dynamical Systems (math.DS)
Linear instability
Instability
Periodic orbits, Non-autonomous Lagrangian functions, Linear instability, Maslov index, Spectral flow
symbols.namesake
FOS: Mathematics
Periodic orbits
Mathematics - Dynamical Systems
Mathematics::Symplectic Geometry
Legendre polynomials
Mathematical Physics
Mathematics
58E10, 53C22, 53D12, 58J30
Applied Mathematics
Mathematical analysis
Regular polygon
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Riemannian manifold
Non-autonomous Lagrangian functions
Orientation (vector space)
Maslov index
Poincaré conjecture
Spectral flow
symbols
Subjects
Details
- ISSN :
- 13616544 and 09517715
- Volume :
- 34
- Database :
- OpenAIRE
- Journal :
- Nonlinearity
- Accession number :
- edsair.doi.dedup.....c14eea87ded348b2e649314f184d3ca9