scholarly journals Comment on ‘‘Theory of the Liapunov exponents of Hamiltonian systems and a numerical study on the transition from regular to irregular classical motion’’

1987 ◽  
Vol 86 (12) ◽  
pp. 7248-7249
Author(s):  
Luis Conde ◽  
Victor Fairén ◽  
Vicente López
Keyword(s):  
Hamiltonian Systems ◽  
Numerical Study ◽  
Classical Motion ◽  
Liapunov Exponents

BIFURCATIONS AND CHAOS IN HAMILTONIAN SYSTEMS

2010 ◽  
Vol 20 (05) ◽  
pp. 1293-1319 ◽  
Author(s):  
R. BARRIO ◽  
F. BLESA ◽  
S. SERRANO
Keyword(s):  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
State Of The Art ◽  
Numerical Study ◽  
Crash Test ◽  
Computational Techniques ◽  
Qualitative Properties ◽  
Numerical Integrations ◽  
Taylor Series Method ◽  
Symmetric Periodic Orbits

This paper deals with the use of recent computational techniques in the numerical study of qualitative properties of two degrees of freedom of Hamiltonian systems. These numerical methods are based on the computation of the OFLI2 Chaos Indicator, the Crash Test and exit basins and the skeleton of symmetric periodic orbits. As paradigmatic examples, three classical problems are studied: the Copenhagen and the (n + 1)-body ring problems and the Hénón–Heiles Hamiltonian. All the numerical integrations have been done by using the state-of-the-art numerical library TIDES based on the extended Taylor series method.

Sign in / Sign up

Export Citation Format

Share Document