Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues

1974 ◽  
Vol 8 (4) ◽  
pp. 435-443 ◽  
Author(s):  
N. Burgoyne ◽  
R. Cushman
Keyword(s):  
Hamiltonian Systems ◽  
Normal Forms ◽  
Linear Hamiltonian Systems ◽  
Real Linear

Stability radii for real linear Hamiltonian systems with perturbed dissipation

2017 ◽  
Vol 57 (3) ◽  
pp. 811-843 ◽  
Author(s):  
Christian Mehl ◽  
Volker Mehrmann ◽  
Punit Sharma
Keyword(s):  
Hamiltonian Systems ◽  
Linear Hamiltonian Systems ◽  
Real Linear ◽  
Stability Radii

ON THE CONSTRUCTION OF TRANSFORMATIONS OF LINEAR HAMILTONIAN SYSTEMS TO REAL NORMAL FORMS

2000 ◽  
Vol 10 (09) ◽  
pp. 2177-2191
Author(s):  
ERIC A. BUTCHER ◽  
S. C. SINHA
Keyword(s):  
Normal Form ◽  
Hamiltonian Systems ◽  
Normal Forms ◽  
Jordan Form ◽  
The Real ◽  
Permutation Matrices ◽  
Linear Hamiltonian Systems ◽  
Symplectic Basis ◽  
Difficult Cases ◽  
Degenerate Cases

A technique for constructing the transformations to real Hamiltonian normal forms of linear Hamiltonian systems via permutation matrices is presented. In particular, a method is shown for obtaining the symplectomorphism between the symplectic basis of the real Jordan form to the standard symplectic basis in which the real Hamiltonian normal form resides. All possible degeneracies are accounted for since the algebraic and geometric multiplicities of nonsemisimple eigenvalues are not restricted, including the "difficult" cases of zero and imaginary eigenvalues. Since the normal forms are not unique, several possible arrangements of the suggested transformations are given which result in the various normal forms derived previously as well as in a few new ones for degenerate cases which have not appeared before.

scholarly journals Oscillation of linear Hamiltonian systems

2002 ◽  
Vol 44 (10-11) ◽  
pp. 1467-1477 ◽  
Author(s):  
Fanwei Meng ◽  
Yuangong Sun
Keyword(s):  
Hamiltonian Systems ◽  
Linear Hamiltonian Systems
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