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Abstract: We show how to build efficient symplectic integrators for polynomial Hamiltonian systems. The efficiency of a numerical method depends both on its computational cost as well as on its accuracy. Polynomial Hamiltonians are separable in exactly solvable parts in many different ways, and we will study how to find a separation for the Hamiltonian in a few number of cheap terms. The new methods will depend on some free parameters and we will also indicate how to choose these parameters in... (Update)
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BibTeX entry: (Update)
@misc{ blanes-symplectic,
author = "Sergio Blanes",
title = "Symplectic Integrators for Polynomial Hamiltonians with Applications to
Accelerator Physics",
url = "citeseer.ist.psu.edu/blanes01symplectic.html" }
Citations (may not include all citations):66 Construction of higher order symplectic integrators (context) - Yoshida - 1990
52 Numerical Hamiltonian Problems (context) - Sanz-Serna, Calvo - 1994
28 Fourth-order symplectic integration (context) - Forest, Ruth - 1990
23 A canonical integration technique (context) - Ruth - 1983
17 Lie series and invariant functions for analytic symplectic m.. (context) - Dragt, Finn - 1976
13 Fractal decomposition of exponential operators with applicat.. (context) - Suzuki - 1990
5 Symplectic integrators with processing: a general study (context) - Blanes, Casas et al. - 1999
5 University of Maryland (context) - Abell, Thesis - 1995
5 Lectures on non linear orbit dynamics (context) - Dragt - 1982
3 Symplectic maps and computation of orbits in particle accele.. (context) - Dragt, Abell - 1996
2 Practical Symplectic Partitioned Runge-- Kutta and Runge--Ku.. - Blanes, Moan - 2000
2 A multi-kick factorization algorithm for nonlinear maps (context) - Irwin - 1989
2 Lie Methods for Nonlinear Dynamics with Applications to Acce.. (context) - Dragt - 1998
2 Variations on a theme by Euler (context) - Feng, Wang - 1998
1 Monomial factorisation of symplectic maps (context) - Gjaja - 1994
1 Computation of maps for particle and light optics by scaling (context) - Dragt - 1995
1 Symplectic completion of symplectic jets (context) - Rangarajan - 1996
1 Explicit integrable Hamiltonians and evaluation of Lie trans.. (context) - Shi, Yan - 1993
1 Integrable polynomial factorisation for symplectic systems (context) - Shi - 1994
1 Jolt factorisation of pendulum map (context) - Rangarajan - 1998
1 Solvable map representation of a nonlinear symplectic map (context) - Rangarajan, Dragt et al. - 1990
1 Symplectic integration using solvable maps (context) - Rangarajan, Sachidanand - 2000
1 Formal Calculus for Lie Methods in Hamiltonian Mechanics (context) - Koseleff - 2030
1 Comment on the exact evaluation of symplectic maps (context) - Michelotti - 1992
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