Pedro Antonio Santoro Salomão

• Abstract

  This project is a continuation of two previous thematic projects supported by FAPESP with numbers 2006/03829-2 and 2011/16265-8. The present group includes researchers working on dynamical systems and low-dimensional geometry and has senior as well as and young researchers, including recent hires. The areas covered by the project are: dynamics in dimension 2: dynamics of homeomorphisms an…

  Dynamics and geometry in low dimensions, AP.TEM

• Abstract

  Since the works of Poincaré and Birkhoff global cross sections are used to study Hamiltonian dynamics restricted to energy levels. Modern methods in Sympletic Dynamics provide an alternative way to study dynamics when such cross sections do not exist. The so called systems of transversal sections are codimension 1 singular foliations of the energy level whose singularity is formed by fini…

  Systems of transversal sections for 3-dimensional Reeb flows, AP.R

• Abstract

  Recent methods in symplectic topology, such as pseudo-holomorphic curves, constitute one of the most advanced tools for studying conservative dynamics. Several classical problems in dynamics can be attacked using these tools, such as geodesic flows, Hamiltonian dynamics etc. In this project, I plan to keep researching in this new area, called symplectic dynamics, proving results for Reeb …

  Symplectic dynamics in dimension 3, AP.R

(Only some records are available in English at this moment)

• Abstract

  The classification of the Reeb flows which are Anosov and have smooth stable and unstable bundels was given by Benoist-Foulon-Labourie (BFL) in 1992. They showed that, up to finite covering and/or reparametrization, such flows are smoothly conjugated to geodesic flows on manifolds with (constant) negative curvature. The goal of this project is to continue the work started on the PhD thesi…

  Geometric conditions for rigidity of Anosov actions, BP.PD

• Abstract

  Embedded contact homology is one of the most powerful tools in symplectic topology. The symplectic capacities originated from this theory are used to study Reeb dynamics and the existence of symplectic embeddings. The goal of this project is to compute the symplectic capacities of some particular cases of symplectic manifolds. (AU)

  Embbeded contact homology and Reeb dynamics, BP.PD

• Abstract

  Pseudo-holomorphic curves have been shown to be an effective tool to atack problems in Hamiltonian dynamics. In this project, we study the existence of finite energy foliations associated to Reeb flows on co-orientable contact manifolds.

  Reeb flows and finite energy foliations, BP.DR

(Only some records are available in English at this moment)

• Abstract

  The study of systolic inequalities for Reeb flows in dimension 3 has been very active recently. The ratio of the square of the least action of a closed Reeb orbit and the contact volume is called the systolic ratio. It is a difficult question to determine upper bounds of the systolic ratio for certain classes of Reeb flows. In general, no such upper bound exists. In this project we intend…

  Systolic inequalities for Reeb flows in dimension 3, BE.PQ

• Abstract

  Study the existence of finite energy foliations in the symplectization of a co-oriented contact manifold admitting periodic orbits with certain properties. (AU)

  Existence o finite energy foliations on symplectizations of contact manifolds, BE.PQ