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Symplectic integration of Hamiltonian systems - Eaton.math.rpi.edu
We refer to these as symplectic integration algorithms (SIAS). ..... However, stable structures, such as the invariant tori of the KAM theorem or stable and unstable ...
[ Chanell_Scovel_90.pdf - Read/Download File

KAM theory and Geometric Integration
stable orbits and KAM tori, possibly of infinite dimension, and a number of ... numerical discrete trajectory associated with a symplectic integrator applied to a  ...
[ report11w5132.pdf - Read/Download File

Survey of Symplectic Integrators
The name symplectic integrator is usually attached to a numer- .... A map ψh,H is called a symplectic integrator if it pre- ..... See [3] for more details on KAM. 8 ...
[ markiewicz.pdf - Read/Download File

Preservation and destruction of periodic orbits by symplectic
Nov 20, 2009 ... Keywords Periodic orbit · Lower dimensional invariant tori · KAM theory · ... When a symplectic integrator using step size h is applied to a ...
[ NumerAlg53.pdf - Read/Download File

Symplectic integration for the collisional gravitational $ N $-body
ABSTRACT. We present a new symplectic integrator designed for collisional gravitational N-body ...... new invariant KAM tori under symplectic discretization ( see.
[ 1503.02728 - Read/Download File

A minimal-coordinate symplectic integrator on spheres arXiv
Feb 10, 2015 ... A globally defined symplectic integrator on S2 needs a minimum of three ...... [31] Z. Shang, KAM theorem of symplectic algorithms for ...
[ 1402.3334 - Read/Download File

Symplectic integration with floating-point - Purdue University
Keywords: Symplectic integration; Floating-point arithmetic; Lattice maps; Leapfrog method. 1. Introduction .... a consequence of KAM theory [17]. Symplectic ...
[ 99Skee.pdf - Read/Download File

Classical Mechanics and Symplectic Integration - University of Hawaii
Classical Mechanics and Symplectic. Integration. −1. −0.5. 0. 0.5. 1. 1.5. −1.5 ... 3.4.1 The KAM Theorem . . . . . . . . . . . . . . . . . . . . 33 ... 3.5 Symplectic Integrators .
[ lecture_notes.pdf - Read/Download File

Six Lectures on the Geometric Integration of ODEs
H. Yoshida, Construction of higher order symplectic integrators, Phys. ..... are most of the invariant circles, as promised by KAM theory for symplectic integrators .
[ talks.pdf - Read/Download File

Symplectic Time-Stepping for Particle Methods - Imperial College
integration as applicable to conservative systems of interacting particles. Such parti- ... which is the most popular symplectic integration method, in §3. Throughout the ...... On the KAM and Nekhoroshev theorems for symplectic integrators and.
[ 04_1.pdf - Read/Download File

Numerical Geometric Integration
IV Symplectic Integration. 51 ... IV.10 Symplectic Integrators on Manifolds . .... explained in Chapter V. If time permits, we also consider KAM theory (Chapter VI) .
[ simplecticos2.pdf - Read/Download File

Symplectic TimeStepping for Particle Methods - Wiley Online Library
Key words Symplectic integration, Hamilton's dynamics, Störmer-Verlet method, ...... On the KAM and Nekhoroshev theorems for symplectic integrators and.
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The accuracy of symplectic integrators - CiteSeerX
case, we con rm several of their properties expected from KAM theory; ... In 6] Feng provides a discussion of the philosophy and history of symplectic integration.
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An unconventional symplectic integrator of W. Kahan - ScienceDirect
An unconventional symplectic integrator of W. Kahan. This paper is dedicated to .... the computed points do not spiral. This is guaranteed by the KAM theory [2].
[ 1-s2.0-0168927494000301-main.pdf?_tid=24dec068-3210-11e5-95f3-00000aab0f02&acdnat=1437748242_c0a952ac2281e9c642f0a1762734cb52 - Read/Download File

High Order Three Part Split Symplectic Integration Schemes
Jun 4, 2013 ... Abstract: Symplectic integration methods based on operator splitting are well ...... [31] Aubry, S. (2011), “KAM tori and absence of diffusion of a ...
[ 24937500.pdf - Read/Download File

between this and the other aspects of the subject that makes - jstor
A turning point in the history of symplectic integrators came in 1988, when ... to wade into the deep waters of symplectic geometry or the KAM theory-a.
[ 2153506 - Read/Download File

implementing arbitrarily high-order symplectic methods via krylov
The symplectic numerical methods are specially designed for integrating ..... spectral integration matrix independent of h as discussed in [12], and can be ...... Z.J. Shang, KAM theorem of symplectic algorithms for Hamiltonian systems, Numer.
[ 0707.pdf - Read/Download File

Symplectic maps
namics is called a symplectic integrator. A first order symplectic .... Aubry–Mather theory gives a nonperturbative generalization of KAM theory for the case of ...
[ SympMaps.pdf - Read/Download File

Why geometric numerical integration? - damtp - University of
Dec 16, 2015 ... context of symplectic integration. • Variational .... KAM-tori, incompressibility, and, most importantly, is a crucial ingredient for ergod- icity.
[ NA2015_05.pdf - Read/Download File

Study of variational symplectic algorithms for the numerical
numerical integration of guiding center equations of motion. Relatore: ..... particle dynamics: as we will discuss later, they are KAM tori of Hamiltonian systems.
[ 2014_Filippo-Zonta.pdf - Read/Download File

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