Work

The Ruelle invariant and convexity in higher dimensions

Year: 2025

Type: article

Abstract: We construct the Ruelle invariant of a volume preserving flow and a symplectic cocycle in any dimension and prove several properties. In the special case of the linearized Reeb flow on the boundary of a convex domain X in \mathbb{R}^{2n} , we prove that the Ruelle invariant \operatorname{Ru}(X) , the period of the systole c(X) and the volume \operatorname{vol}(X) satisfy \operatorname{Ru}(X) \cdot c(X) \le C(n) \cdot \operatorname{vol}(X) . Here C(n) > 0 is an explicit constant depending on n . As an application, we construct dynamically convex contact forms on S^{2n-1} that are not convex, disproving the equivalence of convexity and dynamical convexity in every dimension.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1671

Authors: Julian Chaidez, Oliver Edtmair

Institutions: University of Southern California, University of California, Berkeley

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4412918382

FWCI: 1.636

Cites:

Cited by: 1

Related to: 10