Geometry Seminar
Parabolic saddles and Newhouse domains in Celestial Mechanics
Speaker: Miguel Garrido (Universidad Autónoma de Barcelona)Date: Wednesday, 21 May 2025 - 11:30Place: Aula Naranja, ICMAT
Abstract:
Consider a one-parameter family of smooth surface diffeomorphisms unfolding a quadratic homoclinic tangency to a hyperbolic fixed point. It is a classical result that in this unfolding there exists a Newhouse domain, i.e. an open set of parameters for which the corresponding diffeomorphisms exhibit persistent homoclinic tangencies.
We prove that, for an area preserving map coming from a particular model in Celestial Mechanics, there exists a degenerate parabolic saddle with a quadratic homoclinic tangency which unfolds generically as we move the masses of the bodies. Moreover, and despite the fact that the C^1 Lambda lemma does not hold for this parabolic saddle, we show that the dynamics at the unfolding of the tangency can be renormalized to the Hénon map. This enables recovering the classical results in this degenerate setting.
This is joint work with Pau Martín and Jaime Paradela.
