| Part 1/3 |
Maps and their orbits. Cycles and fixed
points (00:00) Hyperbolic fixed points (13:20) Topological equivalence of maps (19:40) Critical stability cases: Fold (LP), Period-Doubling (PD), and Neimark-Sacker (NS) points (27:16) Center manifold reduction (32:50) Fixed points of parameter-dependent maps. Detection of LP, PD, and NS bifurcations (37:20) |
| Part 2/3 |
Normal forms on center manifolds for LP, PD,
and NS bifurcations (00:00) General method for computation of the critical normal form coefficients (35:30) Critical normal form coefficient for LP (43:00) Critical normal form coefficient for PD (48:38) |
| Part 3/3 |
Critical normal form coefficient for NS
(01:05) |