Conformal Hamiltonian systems

DOI10.1016/S0393-0440(01)00020-1zbMath1005.53058MaRDI QIDQ5959632

Robert I. Mclachlan, Matthew Perlmutter

Publication date: 17 February 2003

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemsPoisson manifoldsymplectic manifold

Mathematics Subject Classification ID

Related Items (39)

On the role of geometry in statistical mechanics and thermodynamics. I. Geometric perspective ⋮ Generalized conformal Hamiltonian dynamics and the pattern formation equations ⋮ Multi-conformal-symplectic PDEs and discretizations ⋮ Metriplectic structure, Leibniz dynamics and dissipative systems ⋮ Second order conformal symplectic schemes for damped Hamiltonian systems ⋮ Deformed Hamiltonian vector fields and Lagrangian fibrations ⋮ A linearly-implicit and conservative Fourier pseudo-spectral method for the 3D Gross-Pitaevskii equation with angular momentum rotation ⋮ Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise ⋮ Friction-adaptive descent: a family of dynamics-based optimization methods ⋮ Analysis of the damped nonlinear space-fractional Schrödinger equation ⋮ Functional equivariance and conservation laws in numerical integration ⋮ On geometry of multiscale mass action law and its fluctuations ⋮ Conformal invariance and conserved quantities of nonmaterial volumes ⋮ Structure-preserving integrators for dissipative systems based on reversible– irreversible splitting ⋮ A KAM theory for conformally symplectic systems: efficient algorithms and their validation ⋮ Jacobi–Maupertuis metric and Kepler equation ⋮ Stability of forced–damped response in mechanical systems from a Melnikov analysis ⋮ Geometric integration of Hamiltonian systems perturbed by Rayleigh damping ⋮ On Extensions, Lie-Poisson Systems, and Dissipations ⋮ Structure-preserving stochastic conformal exponential integrator for linearly damped stochastic differential equations ⋮ Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces ⋮ Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics ⋮ Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System ⋮ On time-dependent Hamiltonian realizations of planar and nonplanar systems ⋮ Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method ⋮ A Conformal Energy-Conserved Method for Maxwell’s Equations with Perfectly Matched Layers ⋮ Structure-preserving Exponential Runge--Kutta Methods ⋮ Hamiltonian formulation of the spin-orbit model with time-varying non-conservative forces ⋮ Euler-Poincaré flows and Leibniz structure of nonlinear reaction-diffusion type systems ⋮ Exponential integrators based on discrete gradients for linearly damped/driven Poisson systems ⋮ Projected exponential Runge-Kutta methods for preserving dissipative properties of perturbed constrained Hamiltonian systems ⋮ Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems ⋮ Generalized conformal symmetries and its application of Hamilton systems ⋮ Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci ⋮ On dissipative symplectic integration with applications to gradient-based optimization ⋮ Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations ⋮ Stochastic conformal schemes for damped stochastic Klein-Gordon equation with additive noise ⋮ Conformal symplectic and relativistic optimization ⋮ Structure-preserving deep learning

Cites Work

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