The Hamiltonian Hopf bifurcation

1985 ◽  
pp. 66-83 ◽  
Author(s):  
Jan-Cees van der Meer
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian Hopf Bifurcation

scholarly journals Splitting of the separatrices after a Hamiltonian–Hopf bifurcation under periodic forcing

Nonlinearity ◽  
2019 ◽  
Vol 32 (4) ◽  
pp. 1440-1493 ◽  
Author(s):  
E Fontich ◽  
C Simó ◽  
A Vieiro
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Forcing ◽  
Hamiltonian Hopf Bifurcation

scholarly journals Hamiltonian Hopf Bifurcation with Symmetry

2002 ◽  
Vol 163 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Pascal Chossat ◽  
Juan-Pablo Ortega ◽  
Tudor S. Ratiu
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian Hopf Bifurcation

Correction to ``Hamiltonian Hopf Bifurcation with Symmetry''

2003 ◽  
Vol 167 (1) ◽  
pp. 83-84
Author(s):  
Pascal Chossat ◽  
Juan-Pablo Ortega ◽  
Tudor S. Ratiu
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian Hopf Bifurcation

scholarly journals THE STRUCTURE AND EVOLUTION OF CONFINED TORI NEAR A HAMILTONIAN HOPF BIFURCATION

2011 ◽  
Vol 21 (08) ◽  
pp. 2321-2330 ◽  
Author(s):  
M. KATSANIKAS ◽  
P. A. PATSIS ◽  
G. CONTOPOULOS
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Orbits ◽  
Transition Point ◽  
Initial Conditions ◽  
Unstable Periodic Orbits ◽  
Unstable Periodic Orbit ◽  
Surface Of Section ◽  
Autonomous Hamiltonian System ◽  
Hamiltonian Hopf Bifurcation ◽  
Stable Periodic

We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unstable. In this paper, we first integrate initial conditions close to the ones of a complex unstable periodic orbit, which is close to the transition point. Then, we plot the consequents of the corresponding orbit in a 4D surface of section. To visualize this surface of section we use the method of color and rotation [Patsis & Zachilas, 1994]. We find that the consequents are contained in 2D "confined tori". Then, we investigate the structure of the phase space in the neighborhood of complex unstable periodic orbits, which are further away from the transition point. In these cases we observe clouds of points in the 4D surfaces of section. The transition between the two types of orbital behavior is abrupt.

On stability at the Hamiltonian Hopf Bifurcation

2009 ◽  
Vol 14 (1) ◽  
pp. 148-162 ◽  
Author(s):  
L. M. Lerman ◽  
A. P. Markova
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian Hopf Bifurcation

scholarly journals The quasi-periodic Hamiltonian Hopf bifurcation

Nonlinearity ◽  
2007 ◽  
Vol 20 (2) ◽  
pp. 417-460 ◽  
Author(s):  
Henk W Broer ◽  
Heinz Hanßmann ◽  
Jun Hoo
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian Hopf Bifurcation
Sign in / Sign up

Export Citation Format

Share Document