Branches of Periodic Orbits in Reversible Systems

2013 ◽  
pp. 39-49 ◽  
Author(s):  
André Vanderbauwhede
Keyword(s):  
Periodic Orbits ◽  
Reversible Systems

Bifurcations of Double Homoclinic Loops in Reversible Systems

2020 ◽  
Vol 30 (16) ◽  
pp. 2050246
Author(s):  
Yuzhen Bai ◽  
Xingbo Liu
Keyword(s):  
Coordinate System ◽  
Periodic Orbits ◽  
Homoclinic Orbit ◽  
Poincaré Map ◽  
Local Coordinate System ◽  
Reversible Systems ◽  
Bifurcation Equation ◽  
Bifurcation Phenomena ◽  
New Type ◽  
Symmetric Periodic Orbits

This paper is devoted to the study of bifurcation phenomena of double homoclinic loops in reversible systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equation, we perform a detailed study to obtain fruitful results, and demonstrate the existence of the R-symmetric large homoclinic orbit of new type near the primary double homoclinic loops, the existence of infinitely many R-symmetric periodic orbits accumulating onto the R-symmetric large homoclinic orbit, and the coexistence of R-symmetric large homoclinic orbit and the double homoclinic loops. The homoclinic bellow can also be found under suitable perturbation. The relevant bifurcation surfaces and the existence regions are located.

CODIMENSION 3 HETEROCLINIC BIFURCATIONS WITH ORBIT AND INCLINATION FLIPS IN REVERSIBLE SYSTEMS

2008 ◽  
Vol 18 (12) ◽  
pp. 3689-3701 ◽  
Author(s):  
YANCONG XU ◽  
DEMING ZHU ◽  
FENGJIE GENG
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Homoclinic Orbit ◽  
Heteroclinic Orbit ◽  
Homoclinic Bifurcation ◽  
Reversible Systems ◽  
Reversible System ◽  
Bifurcation Diagrams ◽  
Symmetric Periodic Orbits ◽  
The Continuum

Heteroclinic bifurcations with orbit-flips and inclination-flips are investigated in a four-dimensional reversible system by using the method originally established in [Zhu, 1998; Zhu & Xia, 1998]. The existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic orbit, R-symmetric homoclinic orbit and R-symmetric periodic orbit are obtained. The double R-symmetric homoclinic bifurcation is found, and the continuum of R-symmetric periodic orbits accumulating into a homoclinic orbit is also demonstrated. Moreover, the bifurcation surfaces and the existence regions are given, and the corresponding bifurcation diagrams are drawn.

Families of periodic orbits in resonant reversible systems

2009 ◽  
Vol 40 (4) ◽  
pp. 511-537 ◽  
Author(s):  
Maurício Firmino Silva Lima ◽  
Marco Antonio Teixeira
Keyword(s):  
Periodic Orbits ◽  
Reversible Systems ◽  
Families Of Periodic Orbits
Sign in / Sign up

Export Citation Format

Share Document