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Inventiones mathematicae, ISSN 0020-9910, 12/2017, Volume 210, Issue 3, pp. 877 - 910
We construct a non-Hamiltonian symplectic circle action on a closed, connected, six-dimensional symplectic manifold with exactly 32 fixed points. 
57S15 | Primary 53D20 | 37J15 | Secondary 14J28 | Mathematics, general | Mathematics | 53D35 | MATHEMATICS | SYMPLECTIC CIRCLE-ACTIONS | MANIFOLDS | PERIODIC FLOWS | CONVEXITY
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2018, Volume 15, Issue 2, pp. 1 - 19
The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range... 
37J15 | 70H50 | 53D05 | Mathematics, general | Mathematics | Lagrangian submanifolds | Lagrangian mechanics | Secondary 70H03 | Primary 53D12 | Mechanics on Lie algebroids | Higher order mechanics | 53D17 | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | TULCZYJEWS TRIPLET | VARIATIONAL-PROBLEMS | Algebra
Journal Article
Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 2018, Volume 40, Issue 6, pp. 1 - 30
Let Q be a closed manifold admitting a locally free action of a compact Lie group G. In this paper, we study the properties of geodesic flows on Q given by... 
2010 Mathematics Subject Classification | 37J15 | 53C35 | 58E05 (Secondary) | 37J45 | 53D20 (Primary) | EXISTENCE | MATHEMATICS | PERIODIC-ORBITS | FIELDS | MATHEMATICS, APPLIED | periodic orbits | symplectic reduction | magnetic flows | Rabinowitz action functional | SYSTEMS | SURFACES | Quotients | Geodesy | Lie groups
Journal Article
Regular and Chaotic Dynamics, ISSN 1560-3547, 9/2019, Volume 24, Issue 5, pp. 525 - 559
We discuss, in all generality, the reduction of a Hamilton — Jacobi theory for systems subject to nonholonomic constraints and invariant under the action of a... 
Hamilton-Jacobi | 37J15 | 37J05 | 35F21 | 53D12 | nonholonomic systems | 53D20 | 37J60 | Mathematics | nonlinear constraints | theory of reduction | 70H20 | symplectic reduction | symmetries | constrained systems | reconstruction | Marsden-Weinstein reduction | Dynamical Systems and Ergodic Theory | Hamilton-Jacobi equations | Research | Holonomy | Mathematical research | Invariants
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 02/2019, Volume 29, Issue 1, pp. 183 - 206
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 2/2019, Volume 55, Issue 1, pp. 17 - 41
Let $$\Xi $$ Ξ be the crown domain associated with a non-compact irreducible Hermitian symmetric space G / K. We give an explicit description of the unique... 
Geometry | Hyper-Kähler manifold | 37J15 | Hermitian symmetric space | 32M15 | Mathematical Physics | Analysis | Crown domain | Global Analysis and Analysis on Manifolds | Mathematics | 53C26 | Differential Geometry | MATHEMATICS | Hyper-Kahler manifold | EXTENSIONS | GRAUERT TUBES | METRICS | COMPLEXIFICATION | COMPLEX STRUCTURES | GEOMETRY | Invariants
Journal Article
Celestial Mechanics and Dynamical Astronomy, ISSN 0923-2958, 5/2019, Volume 131, Issue 5, pp. 1 - 30
Journal Article
Qualitative Theory of Dynamical Systems, ISSN 1575-5460, 8/2019, Volume 18, Issue 2, pp. 371 - 381
The Maxwell–Bloch dissipative equations describe laser dynamics. Under a simple condition on the parameters there exist two time-dependent first integrals,... 
37J15 | Nonstandard separation of variables | Relaxation oscillations | Difference and Functional Equations | Mathematics, general | Mathematics | 78A60 | Dynamical Systems and Ergodic Theory | Dissipative Maxwell–Bloch | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | Dissipative Maxwell-Bloch | INSTABILITIES | Differential equations | Physics
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 6/2016, Volume 26, Issue 3, pp. 787 - 811
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2013, Volume 141, Issue 8, pp. 2809 - 2816
We consider the Hamilton-Jacobi equation H(x, d x u) = c, where c ≥ 0, of the classical N-body problem in some Euclidean space E of dimension at least two. The... 
MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 12/2017, Volume 29, Issue 4, pp. 1283 - 1307
We study the existence of families of periodic solutions in a neighbourhood of a symmetric equilibrium point in two classes of Hamiltonian systems with... 
Liapunov centre theorem | 37J15 | Ordinary Differential Equations | Time-reversing symmetry | Nonlinear normal modes | Mathematics | Applications of Mathematics | 37C27 | Partial Differential Equations | Symmetry | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2013, Volume 18, Issue 6, pp. 832 - 859
We investigate the motion of the point of contact (absolute dynamics) in the integrable problem of the Chaplygin ball rolling on a plane. Although the velocity... 
37J15 | 37J60 | absolute dynamics | Mathematics | nonholonomic constraint | 70K43 | 37J20 | resonance | 70E18 | Dynamical Systems and Ergodic Theory | bifurcation diagram | bifurcation complex | drift | invariant torus | MATHEMATICS, APPLIED | NONHOLONOMIC CHAPLYGIN | EXPLICIT INTEGRATION | PHYSICS, MATHEMATICAL | MECHANICS | DYNAMICS | SYSTEMS | Hamiltonian systems | Motion | Research | Vector spaces | Variables (Mathematics)
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 2/2019, Volume 29, Issue 1, pp. 115 - 138
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 1/2018, Volume 108, Issue 1, pp. 225 - 247
Journal Article
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 12/2016, Volume 26, Issue 6, pp. 1571 - 1613
Journal Article