58Fxx Ordinary differential equations on manifolds; dynamical systems

• 58F03 One-dimensional dynamics, general symbolic dynamics, See also {26A18}
• 58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}
• 58F06 Geometric quantization (applications of representation theory), See also {22E45, 81S10}
• 58F07 Completely integrable systems (including systems with an infinite number of degrees of freedom)
• 58F08 Point-mapping properties, iterations, completeness; dynamics of cellular automata, See also {26A18, 30D05}
• 58F09 Morse-Smale systems
• 58F10 Stability theory
• 58F11 Ergodic theory; invariant measures, See also {28Dxx}
• 58F12 Structure of attractors (and repellors)
• 58F13 Strange attractors; chaos and other pathologies, See Also { 70K50}
• 58F14 Bifurcation theory and singularities
• 58F15 Hyperbolic structures (expanding maps, Anosov systems, etc.)
• 58F17 Geodesic and horocycle flows
• 58F18 Relations with foliations
• 58F19 Eigenvalue and spectral problems
• 58F20 Periodic points and zeta functions
• 58F21 Limit cycles, singular points, etc.
• 58F22 Periodic solutions
• 58F23 Holomorphic dynamics, See also {30D05}
• 58F25 Flows
• 58F27 Quasiperiodic flows
• 58F30 Perturbations
• 58F32 Functional-differential equations on manifolds
• 58F35 Invariance properties
• 58F36 Normal forms
• 58F37 Correspondences and other transformation methods (e.g. Lie-Backlund)
• 58F39 Dynamical systems treatment of PDE (should be assigned another number from 58F), See also {35B32, 35K57}
• 58F40 Applications
• 58F99 None of the above but in this section