Coherent Riemannian-geometric description of Hamiltonian order and chaos with Jacobi metric

DOI10.1063/1.5119797zbMath1473.37073arXiv1906.08146OpenAlexW2951420393WikidataQ92362581 ScholiaQ92362581MaRDI QIDQ5213542

Loris Di Cairano, Matteo Gori, Marco Pettini

Publication date: 3 February 2020

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.08146

zbMATH Keywords

geodesic flowsHamiltonian flowsNewtonian dynamicsJacobi metric

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (3)

The geometric theory of phase transitions ⋮ Chaos indicator and integrability conditions from geometrodynamics ⋮ Hamiltonian chaos and differential geometry of configuration space-time

Cites Work

• On the normal exponential map in singular conformal metrics
• Geometry and topology in Hamiltonian dynamics and statistical mechanics
• Morse theory for geodesics in singular conformal metrics
• Global bifurcations and chaos. Analytical methods
• Proof of the Poincaré-Birkhoff fixed point theorem
• Who's afraid of the Hill boundary?
• Periodische Bewegungen mechanischer Systeme
• On the Riemannian description of chaotic instability in Hamiltonian dynamics
• Non-affine geometrization can lead to non-physical instabilities

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