Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

Abstract

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered.

References in corpus (2)

• Symmetry, singularities and integrability in complex dynamics I: the reduction problem
• Symmetries of homogeneous cosmologies

Cited by in corpus (6)

• Nonlinear Ordinary Differential Equations: A discussion on Symmetries and Singularities
• Symmetry, singularities and integrability in complex dynamics V: Complete symmetry groups of certain relativistic spherically symmetric systems
• Approximate Noether Symmetries and Collineations for Regular Perturbative Lagrangians
• A Study of the Approximate Singular Lagrangian -- Conditional Noether Symmetries and First Integrals
• Symmetry, singularities and intregrability in complex dynamics VII: Integrability Properties of FRW-Scalar Cosmologies
• Symmetry, Singularities and Integrability in Complex Dynamics IV: Painleve Integrability of Isotropic Cosmologies