Galoisian obstructions to integrability and Melnikov criteria for chaos in two-degree-of-freedom Hamiltonian systems with saddle centres

Nonlinearity ◽  
2003 ◽  
Vol 16 (6) ◽  
pp. 2003-2012 ◽  
Author(s):  
Kazuyuki Yagasaki
Keyword(s):  
Hamiltonian Systems ◽  
Degree Of Freedom ◽  
Two Degree Of Freedom

Complexity in spatio-temporal dynamics

1995 ◽  
Vol 125 (5) ◽  
pp. 959-974 ◽  
Author(s):  
D. L. Rod ◽  
B. D. Sleeman
Keyword(s):  
Dynamical Systems ◽  
Hamiltonian Systems ◽  
Temporal Dynamics ◽  
Degree Of Freedom ◽  
Kovacic Algorithm ◽  
Spatio Temporal ◽  
Two Degree Of Freedom

Complex and chaotic structures in certain dynamical systems in biology arise as a consequence of noncomplete integrability of two-degree-of-freedom Hamiltonian systems. A study of this problem is made using Ziglin theory and implemented with the aid of the Kovacic algorithm.

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