| Part 1/4 |
Generic homoclinic orbits to hyperbolic
equilibria (4:26) Andronov-Leontovich Theorem: Saddle homoclinic bifurcations in 2D systems (31:00) Shilnikov Theorems: Saddle and saddle-focus homoclinic bifurcations in 3D generating one cycle (38:20) |
| Part 2/4 |
Shilnikov's Chaos: Saddle-focus and
focus-focus homoclinic bifurcations in 3D and 4D systems
(0:50) |
| Part 3/4 |
Homoclinic problem on the line (0:00) Truncated homoclinic BVP with projection boundary conditions (4:40) Convergence of truncated problem (24:40) Homotopy method to find a homoclinic solution in 3D systems (30:17) |
| Part 4/4 |
Final remarks on continuation of homoclinic
orbits (0:00) |