Hyperbolic characteristics on star-shaped hypersurfaces (Q1961845)

This paper studies the stability of closed characteristics on a star-shaped compact smooth hypersurface \(D\) in \(\mathbb{R}^{2n}\). The authors prove that on \(D\) either there are infinitely many closed characteristics or there exists at least one hyperbolic closed characteristic. The last statement is valid, if every closed characteristic possesses its Maslov-type mean index greater than 2 when \(n\) is odd, and greater than 1 when \(n\) is even.