8 papers
Convex hypersurfaces and robust heterodimensional dynamics
Julian Chaidez, Michael Huang
We prove that any closed orientable hypersurface in a contact manifold of dimension five or greater is isotopic to a robustly non-convex hypersurface via an arbitrarily -small…
Conformally symplectic topology from a dynamical viewpoint
Julian Chaidez
This survey article discusses the emerging interaction between conformally symplectic topology and dynamics, with a focus on recent developments in convex hypersurface theory.
Pseudo-Anosov Reeb flows and contact structures
Julian Chaidez, Yijie Pan
We introduce the notion of a pseudo-Anosov contact structure, which admits a type of singular contact form with pseudo-Anosov Reeb flow. We prove that contact homology detects the…
On dynamical invariants of coadjoint orbits of 3D volume-preserving diffeomorphisms
Robert Cardona, Julian Chaidez, Francisco Torres de Lizaur
The helicity, or asymptotic linking number, is a functional of exact volume-preserving vector fields on 3-manifolds, invariant under volume-preserving transformations. It is known…
Contact homology and linearization without dga homotopies
Julian Chaidez
This article clarifies the status of linearized contact homology given the foundations of the contact dg-algebra established by Pardon. In particular, we prove that the set of isom…
Robustly non-convex hypersurfaces in contact manifolds
Julian Chaidez
We construct the first examples of hypersurfaces in any contact manifold of dimension 5 and larger that cannot be -approximated by convex hypersurfaces, contrasting sharply wi…