Výsledky vyhledávání - "Pedro A. S. Salomão"

Global surfaces of section with positive genus for dynamically convex Reeb flows

Autor: Umberto L. Hryniewicz, Pedro A. S. Salomão, Richard Siefring

Publikováno v: Journal of fixed point theory and applications : JFPTA 24(2), 45 (2022). doi:10.1007/s11784-022-00950-z
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

We establish some new existence results for global surfaces of section of dynamically convex Reeb flows on the three-sphere. These sections often have genus, and are the result of a combination of pseudo-holomorphic curve methods with some elementary

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b811f1468c24159b587d01f91ac2ac63
https://publications.rwth-aachen.de/record/848251

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Contact forms with large systolic ratio in dimension three

Autor: Alberto Abbondandolo, Pedro A. S. Salomão, Umberto L. Hryniewicz, Barney Bramham

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every co-orientable contact structure on any closed three-manifold is defin

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97f86efc8a8f7a6530292e95a746ddff
https://doi.org/10.2422/2036-2145.201709_005

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Systems of Transversal Sections near Critical Energy Levels of Hamiltonian Systems in ℝ⁴

Autor: Naiara V. de Paulo, Pedro A. S. Salomão

Publikováno v: Memoirs of the American Mathematical Society. 252

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a3bcb24f4f14e6128704a89b06efbbf2
https://doi.org/10.1090/memo/1202

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Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere

Autor: Alberto Abbondandolo, Barney Bramham, Pedro A. S. Salomão, Umberto L. Hryniewicz

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validity would imply that the systolic ratio of a convex contact form does no

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Sharp systolic inequalities for Riemannian and Finsler spheres of revolution

Autor: Alberto Abbondandolo, Barney Bramham, Pedro A. S. Salomão, Umberto L. Hryniewicz

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

We prove that the systolic ratio of a sphere of revolution $S$ does not exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we consider the rotationally symmetric Finsler metrics on a sphere of revolution which are defined by sh

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Elektronická kniha

Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb

Autor: Naiara V. de Paulo, Pedro A. S. Salomão

In this article the authors study Hamiltonian flows associated to smooth functions $H:\mathbb R^4 \to \mathbb R$ restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point $p_c$ in the zero en

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Global surfaces of section for Reeb flows in dimension three and beyond

Autor: Pedro A. S. Salomão, Umberto L. Hryniewicz

We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to geometry, including existence of closed geodesics and sharp systolic

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On the multiplicity of periodic orbits and homoclinics near critical energy levels of Hamiltonian systems in $\mathbb{R}^4$

Autor: Naiara V. de Paulo, Pedro A. S. Salomão

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

We study two-degree-of-freedom Hamiltonian systems. Let us assume that the zero energy level of a real-analytic Hamiltonian function $H:\mathbb{R}^4 \to \mathbb{R}$ contains a saddle-center equilibrium point lying in a strictly convex sphere-like sin

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Sharp systolic inequalities for Reeb flows on the three-sphere

Autor: Pedro A. S. Salomão, Umberto L. Hryniewicz, Barney Bramham, Alberto Abbondandolo

Publikováno v: Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP

The systolic ratio of a contact form $\alpha$ on the three-sphere is the quantity \[ \rho_{\mathrm{sys}}(\alpha) = \frac{T_{\min}(\alpha)^2}{\mathrm{vol}(S^3,\alpha\wedge d\alpha)}, \] where $T_{\min}(\alpha)$ is the minimal period of closed Reeb orb

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