Partially hyperbolic dynamics in the 3-body problem

TL;DR

This paper constructs symplectic blenders for the 3-body problem and its restricted version, demonstrating robust topological instability without smallness assumptions on masses, using novel abstract results on twist maps and skew-products.

Contribution

It introduces a new method to show topological instability in classical Hamiltonian systems via symplectic blenders and abstract twist map results.

Findings

Demonstrates robust topological instability in the 3-body problem

Constructs symplectic blenders for Hamiltonian systems

Provides explicit conditions for transitivity in twist maps

Abstract

We construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. We use these objects to show that both models exhibit a robust, strong form of topological instability. We do not assume any smallness conditions on the masses but require only that at least two of them are distinct. Our construction is based on two abstract results which might be of independent interest. The first one gives an explicit condition under which a given pair of twist maps of the cylinder generates a locally transitive iterated function system. The second one extends this result to certain cylinder skew-products.