Part 1/3
Homoclinic orbits to fixed points of maps (3:00)
Stable and unstable invariant sets of hyperbolic fixed points (9:30)
Hetero-/homoclinic orbits as intersections of stable and unstable invariant manifolds (11:50)
Regular homoclinic orbits (32:00)
Poincare-Birkhoff-Smale-Shilnikov Theorem (35:00)
Homoclinic tangency (42:00)
Part 2/3
Continuation of regular homoclinic orbits (2:50)
Computation of 1D unstable invariant manifolds (27:00)
Computation of 1D stable invariant manifolds (47:10)
Part 3/3
Location of homoclinic orbits of planar maps as intersections of 1D invariant manifolds (12:00)