“Auxiliary Lesson” שעור עזר) #7) December 6, 2007

Invariant manifolds for hyperbolic maps. Complex hyperbolicity.

1. Formal theory: cross-resonances.
2. Hadamard-Perron theorem for holomorphisms. Contracting map principle reactivated.
3. Hadamard-Perron theorem for vector fields. Complex hyperbolicity.
4. Invariant hypernolic curve for saddle-nodes.
5. Poincare resonances.
6. Center manifolds: formal but non-analytic.

Reading: Section 7 from the book (printing disabled), Section 27 (parts A-C) from the book (printing disabled)

Disclaimer is as sadly relevant as before…