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Symplectic dynamics in dimension 3


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 dynamics in dimension 3, such as existence and multiplicity of periodic orbits, existence of systems of transversal sections to the flow, dynamical characterizations of contact manifolds, and may other things. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
ABBONDANDOLO, ALBERTO; BRAMHAM, BARNEY; HRYNIEWICZ, UMBERTO L.; SALOMAO, PEDRO A. S.. A systolic inequality for geodesic flows on the two-sphere. MATHEMATISCHE ANNALEN, v. 367, n. 1-2, p. 701-753, . (13/20065-0)
DE PAULO, NAIARA V.; SALOMAO, PEDRO A. S.. Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R-4. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 252, n. 1202, p. 1+, . (09/18586-6, 14/08113-1, 11/16265-8, 13/20065-0)
HRYNIEWICZ, UMBERTO L.; SALOMAO, PEDRO A. S.. Elliptic bindings for dynamically convex Reeb flows on the real projective three-space. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 55, n. 2, . (13/20065-0, 11/16265-8)

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