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Creators/Authors contains: "Chaidez, Julian"

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  1. ; (, Journal of the European Mathematical Society)
    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 domainXin\mathbb{R}^{2n}, we prove that the Ruelle invariant\operatorname{Ru}(X), the period of the systolec(X)and the volume\operatorname{vol}(X)satisfy\operatorname{Ru}(X) \cdot c(X) \le C(n) \cdot \operatorname{vol}(X). HereC(n) > 0is an explicit constant depending onn. As an application, we construct dynamically convex contact forms onS^{2n-1}that are not convex, disproving the equivalence of convexity and dynamical convexity in every dimension. 
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    Free, publicly-accessible full text available July 25, 2026
  2. ; (, Journal of the London Mathematical Society)
    We develop new methods of both constructing and obstructing symplectic embeddings into nontoric rational surfaces using the theory of Newton–Okoukov bodies. Applications include sharp embedding results for concave toric domains into nontoric rational surfaces, and new cases of nonexistence for infinite staircases in the nontoric setting. 
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  3. ; ; ; (, Journal of Modern Dynamics)
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  4. ; (, Journal of Computational Dynamics)
    null (Ed.)
    We study the combinatorial Reeb flow on the boundary of a four-dimensional convex polytope. We establish a correspondence between "combinatorial Reeb orbits" for a polytope, and ordinary Reeb orbits for a smoothing of the polytope, respecting action and Conley-Zehnder index. One can then use a computer to find all combinatorial Reeb orbits up to a given action and Conley-Zehnder index. We present some results of experiments testing Viterbo's conjecture and related conjectures. In particular, we have found some new examples of polytopes with systolic ratio \begin{document}$ 1 $$\end{document}$. 
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