Embedded Files
I am interested in the relationship between Hamiltonian systems and the geometry and topology of the underlying space. On the one hand, periodic orbits of Hamiltonian systems yield geometric invariants such as symplectic capacities and symplectic homology. On the other hand, using symplectic tools we can understand concrete Hamiltonian systems coming from physics, such as those describing the motion of charged particles in a magnetic field.
I am interested in the relationship between Hamiltonian systems and the geometry and topology of the underlying space. On the one hand, periodic orbits of Hamiltonian systems yield geometric invariants such as symplectic capacities and symplectic homology. On the other hand, using symplectic tools we can understand concrete Hamiltonian systems coming from physics, such as those describing the motion of charged particles in a magnetic field.
Ongoing Projects
Ongoing Projects
Zoll Magnetic Systems on Surfaces (with Alexander Langreiter, Luca Asselle, Massimiliano Berti)
Magnetic Systems on the Torus without Contractible Periodic Orbits (with Alexander Langreiter)
Periodic Magnetic Geodesics on Low Energy Levels (with Valerio Assenza, Leonardo Macarini)
The Cost of Flexibility in Symplectic and Contact Geometry (with Alberto Abbondandolo, Leonid Polterovich)
Lorentz-Finsler Structures on the Lagrangian Grassmannian
Capacities of Hofer-Zehnder type (with Johanna Bimmermann)
Publications
Publications
2026
2026
G. B., J. Bimmermann, S. Sanjay, On the Rigidity of Symplectic Magnetic Systems that are Zoll at Low Energies, in preparation.
A. Abbondandolo, G. B., L. Polterovich, Lorentz–Finsler metrics on symplectic and contact transformation groups, Annali di Scienze (to appear), 105 p.
2025
2025
A. Abbondandolo, G. B., O. Edtmair, Symplectic capacities of domains close to the ball and Banach–Mazur geodesics in the space of contact forms, Duke Mathematical Journal 174 (2025), no. 8, 1567–1646.
P. Albers, G. B., L. Maier, The Hopf-Rinow theorem and the Mañé critical value for magnetic geodesics on odd-dimensional spheres, Journal of Geometry and Physics 214 (2025), Article ID 105521, 21 p.
2024
2024
P. Albers, G. B., An observation about conformal points on surfaces, Arnold Mathematical Journal 10 (2024), no. 4, 473-485.
G. B., J. Bimmermann, K. Zehmisch, Symplectic capacities of disc cotangent bundles of flat tori, Proceedings of the American Mathematical Society 152 (2024), no. 12, 5367-5372.
L. Asselle, G. B., M. Berti, Zoll magnetic systems on the two-torus: a Nash–Moser construction, Advances in Mathematics 452 (2024), Article ID 109826, 39 p.
2023
2023
A. Abbondandolo, G. B., On the local systolic optimality of Zoll contact forms, Geometric and Functional Analysis (GAFA) 33 (2023), no. 2, 299–363.
2022
2022
L. Asselle, G. B., Non-resonant circles for strong magnetic fields on surfaces, Annales Henri Lebesgue 5 (2022), 1191–1211.
G. B., J. Kang, On a systolic inequality for closed magnetic geodesics on surfaces, Journal of Symplectic Geometry 20 (2022), no. 1, 99–134.
G. B., J. Kang, Relative Hofer–Zehnder capacity and positive symplectic homology, Journal of Fixed Point Theory and Applications, 24:44 (2022).
L. Asselle, G. B., Normal forms for strong magnetic systems on surfaces: Trapping regions and rigidity of Zoll systems, Ergodic Theory and Dynamical Systems 42 (2022), no. 6, 1871–1897.
2021
2021
L. Asselle, G. B., M. Mazzucchelli, Minimal boundaries in Tonelli Lagrangian systems, International Mathematical Research Notices 20 (2021), 15746–15787.
L. Asselle, G. B., Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities, The Journal of Geometric Analysis 31 (2021), 2924–2940.
G. B., J. Kang, A local contact systolic inequality in dimension three, Journal of the European Mathematical Society 23 (2021), no. 3, 721–764.
2020
2020
G. B., A. F. Ritter, Invariance of symplectic cohomology and twisted cotangent bundles over surfaces, International Journal of Mathematics 31 (2020), no. 9, 2050070, 56 pages.
G. B., J. Kang, On a local systolic inequality for odd-symplectic forms, Portugaliae Mathematica 76 (2020), no. 3-4, 327–394.
2017
2017
A. Abbondandolo, L. Asselle, G. B., M. Mazzucchelli, I. A. Taimanov, The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere, Advanced Nonlinear Studies 17 (2017), no. 1, 17–30.
L. Asselle, G. B., On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus, Mathematische Zeitschrift 286 (2017), no. 3-4, 843–859.
2016
2016
G. B., On closed orbits for twisted autonomous Tonelli Lagrangian flows, Publicaciones Matemáticas del Uruguay 16 (2016), 41–79.
G. B., Magnetic Katok examples on the two-sphere, Bulletin of the London Mathematical Society 48 (2016), no. 5, 855–865.
L. Asselle, G. B., The Lusternik-Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles, Journal of Topology and Analysis 8 (2016), no. 3, 545–570.
G. B., The contact property for symplectic magnetic fields on S^2, Ergodic Theory and Dynamical Systems 36 (2016), no. 3, 682–713.
2015
2015
G. B., K. Zehmisch, On the existence of periodic orbits for magnetic systems on the two-sphere, Journal of Modern Dynamics 9 (2015), 141–146.
L. Asselle, G. B., Infinitely many periodic orbits of non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level, Calculus of Variations and Partial Differential Equations 54 (2015), no. 2, 1525–1545.
2014
2014
G. B., The contact property for magnetic flows on surfaces (PhD Thesis), University of Cambridge.
Page updated
Google Sites
Report abuse