scholarly journals Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps

Nonlinearity ◽  
2021 ◽  
Vol 34 (5) ◽  
pp. 2897-2918
Author(s):  
Xiaoxue Xu ◽  
Cewen Cao ◽  
Frank W Nijhoff
Keyword(s):  
Geometric Integration ◽  
Symplectic Maps ◽  
Lattice Equation

scholarly journals Transport Barriers in Symplectic Maps

2021 ◽  
Vol 51 (3) ◽  
pp. 899-909
Author(s):  
R. L. Viana ◽  
I. L. Caldas ◽  
J. D. Szezech ◽  
A. M. Batista ◽  
C. V. Abud ◽  
...  
Keyword(s):  
Symplectic Maps ◽  
Transport Barriers

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

Analysis of resonances in action space for symplectic maps

1998 ◽  
Vol 57 (1) ◽  
pp. 1178-1180 ◽  
Author(s):  
A. Bazzani ◽  
L. Bongini ◽  
G. Turchetti
Keyword(s):  
Action Space ◽  
Symplectic Maps

scholarly journals COMMUTATORS OF SKEW-SYMMETRIC MATRICES

2005 ◽  
Vol 15 (03) ◽  
pp. 793-801 ◽  
Author(s):  
ANTHONY M. BLOCH ◽  
ARIEH ISERLES
Keyword(s):  
Optimal Control ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Group ◽  
Geometric Integration ◽  
Symmetric Matrices ◽  
Frobenius Norm

In this paper we develop a theory for analysing the "radius" of the Lie algebra of a matrix Lie group, which is a measure of the size of its commutators. Complete details are given for the Lie algebra 𝔰𝔬(n) of skew symmetric matrices where we prove [Formula: see text], X, Y ∈ 𝔰𝔬(n), for the Frobenius norm. We indicate how these ideas might be extended to other matrix Lie algebras. We discuss why these ideas are of interest in applications such as geometric integration and optimal control.

Sign in / Sign up

Export Citation Format

Share Document