Zobrazeno 1 - 10
of 71
pro vyhledávání: '"SALOMÃO, PEDRO A. S."'
We investigate the dynamics of a two-degree-of-freedom mechanical system for energies slightly above a critical value. The critical set of the potential function is assumed to contain a finite number of saddle points. As the energy increases across t
Externí odkaz:
http://arxiv.org/abs/2409.00445
Publikováno v:
S\~ao Paulo Journal of Mathematical Sciences, v. 16, n. 1, p. 314-339, 2022
Pseudo-holomorphic curves in symplectizations, as introduced by Hofer in 1993, and then developed by Hofer, Wysocki, and Zehnder, have brought new insights to Hamiltonian dynamics, providing new approaches to some classical questions in Celestial Mec
Externí odkaz:
http://arxiv.org/abs/2404.08864
We study the spatial isosceles three-body problem from the perspective of Symplectic Dynamics. For certain choices of mass ratio, angular momentum, and energy, the dynamics on the energy surface is equivalent to a Reeb flow on the tight three-sphere.
Externí odkaz:
http://arxiv.org/abs/2308.00338
A contact form on the tight $3$-sphere $(S^3,\xi_0)$ is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least $2$. In this article, we study Reeb flows of weakly convex contact forms on $(S^3,\xi_0)$ admitting a prescribed
Externí odkaz:
http://arxiv.org/abs/2206.12856
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:
http://arxiv.org/abs/2012.12055
We introduce numerical invariants of contact forms in dimension three and use asymptotic cycles to estimate them. As a consequence, we prove a version for Anosov Reeb flows of results due to Hutchings and Weiler on mean actions of periodic points. Th
Externí odkaz:
http://arxiv.org/abs/2006.06266
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We exhibit sufficient conditions for a finite collection of periodic orbits of a Reeb flow on a closed $3$-manifold to bound a positive global surface of section with genus zero. These conditions turn out to be $C^\infty$-generically necessary. Moreo
Externí odkaz:
http://arxiv.org/abs/1912.01078
Publikováno v:
Trans. Amer. Math. Soc. 374 (2021), 1815-1845
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
Externí odkaz:
http://arxiv.org/abs/1808.06995
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
Externí odkaz:
http://arxiv.org/abs/1712.04720