scholarly journals Homoclinic Orbits to Invariant Tori in Hamiltonian Systems

2001 ◽  
pp. 1-27 ◽  
Author(s):  
Amadeu Delshams ◽  
Pere Gutiérrez
Keyword(s):  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Homoclinic Orbits

Homoclinic orbits for invariant tori of nearly integrable Hamiltonian systems

2006 ◽  
Vol 73 (2) ◽  
pp. 217-220
Author(s):  
O. Yu. Koltsova ◽  
L. M. Lerman ◽  
A. Delshams ◽  
P. Gutiérrez
Keyword(s):  
Hamiltonian Systems ◽  
Invariant Tori ◽  
Homoclinic Orbits ◽  
Integrable Hamiltonian Systems ◽  
Nearly Integrable Hamiltonian Systems

scholarly journals Erratum to: Homoclinic orbits for an unbounded superquadratic Hamiltonian systems

2010 ◽  
Vol 18 (1) ◽  
pp. 115-115
Author(s):  
Jun Wang ◽  
Junxiang Xu ◽  
Fubao Zhang ◽  
Lei Wang
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits

Nontrivial homoclinic orbits for second-order singular and periodic Hamiltonian systems

1999 ◽  
Vol 44 (2) ◽  
pp. 123-129 ◽  
Author(s):  
Chengyue Li ◽  
Tianyou Fan ◽  
Mingsheng Tong
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Second Order

Exact Torus Knot Periodic Orbits and Homoclinic Orbits in a Class of Three-Dimensional Flows Generated by a Planar Cubic System

2017 ◽  
Vol 27 (13) ◽  
pp. 1750205 ◽  
Author(s):  
Tonghua Zhang ◽  
Jibin Li
Keyword(s):  
Vector Field ◽  
Periodic Orbits ◽  
Invariant Tori ◽  
Three Dimensional ◽  
Homoclinic Orbits ◽  
Numerical Examples ◽  
Torus Knot ◽  
Cubic System ◽  
Theoretical Results

This paper considers a class of three-dimensional systems constructed by a rotating planar symmetric cubic vector field. To study its periodic orbits including homoclinic orbits, which may be knotted in space, we classify the types of periodic orbits and then calculate their exact parametric representations. Our study shows that this class of systems has infinitely many distinct types of knotted periodic orbits, which lie on three families of invariant tori. Numerical examples of [Formula: see text]-torus knot periodic orbits have also been provided to illustrate our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document