39 citations · 148 across the 25 of their papers we have counts for
30 papers
Obstruction to Symplectic Embeddings between Toric Domains
Marcelo Miranda, Pedro A. S. Salomão, Jonathan Trejos
We study symplectic embeddings between four-dimensional toric domains using embedded contact homology. Extending Hutchings' criterion for embeddings between convex toric domains, w…
Birkhoff conjecture and finite energy foliations in Hill's lunar problem
Lei Liu, Pedro A. S. Salomão
We prove Birkhoff's retrograde orbit conjecture in Hill's lunar problem by showing that the retrograde orbit bounds a disk-like global surface of section for every energy below the…
Blaschke-type models for multimodal circle maps
Edson de Faria, Welington de Melo, Pedro A. S. Salomão +1
For each integer , we construct a finite-dimensional family of rational maps, given by Blaschke-type products, whose restriction to the unit circle consists of -multi…
Cylindrical contact homology for weakly convex contact forms in dimension three
Ana Kelly de Oliveira, Pedro A. S. Salomão
A contact form on a closed contact three-manifold is called weakly convex if either it has no contractible Reeb orbit, or the first Chern class of vanishes on $π_2(…
ECH Constraints and Twist Dynamics in the Spatial Isosceles Three-Body Problem
Xijun Hu, Lei Liu, Yuwei Ou +2
We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the…
On the knot types of periodic Reeb orbits of dynamically convex contact forms
Umberto L. Hryniewicz, Pedro A. S. Salomão, Richard Siefring
We exhibit transverse knot types on the standard contact -sphere that cannot be realized as periodic Reeb orbits of a dynamically convex contact form. In particular, such transv…
Finite energy foliations and global dynamics in the restricted three-body problem
Lei Liu, Pedro A. S. Salomão
We establish a general criterion for the existence of finite energy foliations on contact three-manifolds with boundary, imposing strong global constraints on the associated Reeb f…
Non-resonant Hopf Links Near a Hamiltonian Equilibrium Point
C. Grotta-Ragazzo, Lei Liu, Pedro A. S. Salomão
This paper is about the existence of periodic orbits near an equilibrium point of a two-degree-of-freedom Hamiltonian system. The equilibrium is supposed to be a nondegenerate mini…
Transverse foliations for two-degree-of-freedom mechanical systems
Naiara V. de Paulo, Seongchan Kim, Pedro A. S. Salomão +1
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 cont…
Reeb flows, pseudo-holomorphic curves and transverse foliations
Naiara V. de Paulo, Pedro A. S. Salomão
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,…
A symplectic dynamics approach to the spatial isosceles three-body problem
Xijun Hu, Lei Liu, Yuwei Ou +2
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…
Genus zero transverse foliations for weakly convex Reeb flows on the tight -sphere
Naiara V. de Paulo, Umberto Hryniewicz, Seongchan Kim +1
A contact form on the tight -sphere is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least . In this article, we study Reeb flows of…
Global surfaces of section with positive genus for dynamically convex Reeb flows
Umberto L. Hryniewicz, Pedro A. S. Salomão, Richard Siefring
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…
On the relation between action and linking
David Bechara Senior, Umberto L. Hryniewicz, Pedro A. S. Salomão
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 resu…
Genus zero global surfaces of section for Reeb flows and a result of Birkhoff
Umberto L. Hryniewicz, Pedro A. S. Salomão, Krzysztof Wysocki
We exhibit sufficient conditions for a finite collection of periodic orbits of a Reeb flow on a closed -manifold to bound a positive global surface of section with genus zero. T…
Sharp systolic inequalities for Riemannian and Finsler spheres of revolution
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
We prove that the systolic ratio of a sphere of revolution does not exceed and equals if and only if is Zoll. More generally, we consider the rotationally symmetric…
On the multiplicity of periodic orbits and homoclinics near critical energy levels of Hamiltonian systems in
Naiara V. de Paulo, Pedro A. S. Salomão
We study two-degree-of-freedom Hamiltonian systems. Let us assume that the zero energy level of a real-analytic Hamiltonian function contains a sadd…
Global surfaces of section for Reeb flows in dimension three and beyond
Umberto L. Hryniewicz, Pedro A. S. Salomão
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…
Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere
Alberto Abbondandolo, Barney Bramham, Umberto Hryniewicz +1
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 validit…
Contact forms with large systolic ratio in dimension three
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
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…
Elliptic bindings for dynamically convex Reeb flows on the real projective three-space
Umberto L. Hryniewicz, Pedro A. S. Salomão
The first result of this paper is that every contact form on sufficiently -close to a dynamically convex contact form admits an elliptic-parabolic closed…
Sharp systolic inequalities for Reeb flows on the three-sphere
A. Abbondandolo, B. Bramham, U. L. Hryniewicz +1
The systolic ratio of a contact form on the three-sphere is the quantity \[ ρ_{\mathrm{sys}}(α) = \frac{T_{\min}(α)^2}{\mathrm{vol}(S^3,α\wedge dα)}, \] where is…
A systolic inequality for geodesic flows on the two-sphere
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
For a Riemannian metric on the two-sphere, let be the length of the shortest closed geodesic and be the length of the longest simple closed ge…
Persistence of fixed points under rigid perturbations of maps
Salvador Addas-Zanata, Pedro A. S. Salomão
Let be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $\…