Perturbation to Lie symmetry and adiabatic invariants for Birkhoffian systems on time scales

DOI10.1016/j.cnsns.2019.04.005OpenAlexW2933752246WikidataQ128121202 ScholiaQ128121202MaRDI QIDQ2206522

Yi Zhang, Xiang-Hua Zhai

Publication date: 22 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2019.04.005

zbMATH Keywords

perturbationadiabatic invariantLie symmetryBirkhoffian system on time scales

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Perturbations of ordinary differential equations (34D10) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Dynamic equations on time scales or measure chains (34N05) Real analysis on time scales or measure chains (26E70) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)

Related Items (5)

A new type of adiabatic invariants for disturbed Birkhoffian system of Herglotz type ⋮ Non-standard Birkhoffian dynamics and its Noether's theorems ⋮ Lie symmetry analysis and conservation law for the equation arising from higher order Broer-Kaup equation ⋮ Mei symmetry and new conserved quantities of time-scale Birkhoff's equations ⋮ Nonshifted dynamics of constrained systems on time scales under Lagrange framework and its Noether's theorem

Cites Work

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• Noether symmetries and conserved quantities for fractional Birkhoffian systems
• The second Euler-Lagrange equation of variational calculus on time scales
• A new type of non-Noether exact invariants and adiabatic invariants of generalized Hamiltonian systems
• Lie symmetries and conservation laws of the Hirota-Ramani equation
• Lie symmetry and conservation law of Birkhoffian system.
• Analysis on measure chains - a unified approach to continuous and discrete calculus
• On the Birkhoffian mechanics
• Adiabatic invariants for dynamical systems with one degree of freedom
• Lie symmetries and conserved quantities of constrained mechanical systems
• Dynamic equations on time scales: A survey
• On the integration methods of nonholonomic dynamics
• Symmetry and integration methods for differential equations
• Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws
• Conserved quantities for Hamiltonian systems on time scales
• Noether theorem for non-conservative systems with time delay on time scales
• Almost periodic dynamics for impulsive delay neural networks of a general type on almost periodic time scales
• Perturbation to Noether symmetries and adiabatic invariants for disturbed Hamiltonian systems based on El-Nabulsi nonconservative dynamics model
• Fractional Birkhoffian mechanics
• Variational problem of Herglotz type for Birkhoffian system and its Noether's theorems
• Perturbation of symmetries of rotational relativistic Birkhoffian systems and its inverse problem
• Lie symmetries, perturbation to symmetries and adiabatic invariants of Lagrange system
• Noether's theorem on time scales
• Dynamical symmetries and conserved quantities
• Noether theorem for Birkhoffian systems on time scales
• On the Lie symmetries of the classical Kepler problem
• A new conservation law constructed without using either Lagrangians or Hamiltonians
• Birkhoffian formulations of nonholonomic constrained systems

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