A geometric proof of the periodic averaging theorem on Riemannian manifolds

DOI10.1007/S13163-015-0184-8zbMath1362.37047arXiv1512.05041OpenAlexW3101843176WikidataQ115376174 ScholiaQ115376174MaRDI QIDQ262643

Guillermo Dávila-Rascón, Misael Avendaño-Camacho

Publication date: 30 March 2016

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.05041

zbMATH Keywords

perturbation theoryRiemannian manifoldaveraging method\(S^1\)-action\(S^1\)-principal bundlehorizontal liftperiodic flow

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Global Riemannian geometry, including pinching (53C20) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Fiber bundles in algebraic topology (55R10) Manifolds of metrics (especially Riemannian) (58D17)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homological equations for tensor fields and periodic averaging
• The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
• Manifolds, tensor analysis, and applications.
• On action-angle variables
• Global Gronwall estimates for integral curves on Riemannian manifolds
• On global action-angle coordinates
• Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems
• Canonical transformations depending on a small parameter
• Regularization of kepler's problem and the averaging method on a manifold
• Sur Les Solutions Périodiques De Certains Systémes Differentiels Perturbés
• Averaging methods in nonlinear dynamical systems
• Riemannian geometry.

This page was built for publication: A geometric proof of the periodic averaging theorem on Riemannian manifolds