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Hamiltonian Systems: Chaos, Integrability and Phase Transition
https://doi.org/10.1142/9789814282253_0006Cited by:0 (Source: Crossref)
Abstract:
The following sections are included:
A Dynamical System with Self-Interaction
Hamiltonian and metric tensor
Geodesic equation
Jacobi equation
Metric and covariant derivative
Two Degrees of Freedom
Potentials
Sectional curvature
Hénon–Heiles Model and Chaos
Conventional method
Evidence of chaos in a geometrical aspect
Geometry and Chaos
Invariants in a Generalized Model
Killing vector field
Another integrable case
Topological Signature of Phase Transitions
Morse function and Euler index
Signatures of phase transition
Topological change in the mean-field XY model
