Morse theory for Hamiltonian systems, 2001. ,
Foundations of mechanics, vol.36, 1978. ,
Shape of vortices for a rotating bose-einstein condensate, Physical Review A, vol.66, issue.2, p.23611, 2002. ,
Finiteness of central configurations of five bodies in the plane, Annals of mathematics, vol.176, pp.535-588, 2012. ,
Motion of three vortices, The Physics of Fluids, vol.22, issue.3, pp.393-400, 1979. ,
Point vortex motions with a center of symmetry. The Physics of Fluids, vol.25, pp.2183-2187, 1982. ,
Vortex crystals, Department of Theoretical and Applied Mechanics, 2002. ,
Point vortices exhibit asymmetric equilibria, Nature, vol.392, issue.6678, p.769, 1998. ,
Mathematical methods of classical mechanics, 1989. ,
, Morse theory and Floer homology, 2014.
Nonintegrability of two problems in vortex dynamics, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.7, issue.3, pp.368-375, 1997. ,
Periodic solutions of the n-vortex hamiltonian system in planar domains, Journal of Differential Equations, vol.260, issue.3, pp.2275-2295, 2016. ,
Global continua of periodic solutions of singular first-order hamiltonian systems of n-vortex type, Mathematische Annalen, vol.369, issue.1-2, pp.627-651, 2017. ,
The morse property for functions of kirchhoff-routh path type, 2017. ,
Critical points of the n-vortex hamiltonian in bounded planar domains and steady state solutions of the incompressible euler equations, SIAM Journal on Applied Mathematics, vol.75, issue.2, pp.726-744, 2015. ,
Action minimizing orbits in the n-body problem with simple choreography constraint, Nonlinearity, vol.17, issue.6, 2004. ,
Critical point theorems for indefinite functionals, Inventiones Mathematicae, vol.52, issue.3, pp.241-273, 1979. ,
Kam theory analysis of the dynamics of three coaxial vortex rings, Physica D, vol.140, pp.321-348, 2000. ,
Lie algebras in vortex dynamics and celestial mechanics-iv, Regular and Chaotic Dynamics, vol.4, issue.1, pp.23-50, 1999. ,
Dynamics of three vorteces on a plane and a sphere-ii. general compact case, Regular and Chaotic Dynamics, vol.3, issue.2, pp.99-114, 1998. ,
Dynamics of three vortices on a plane and a sphere-iii. noncompact case. problems of collaps and scattering, Regular and Chaotic Dynamics, vol.3, issue.4, pp.74-86, 1998. ,
Absolute and relative choreographies in the problem of point vortices moving on a plane, Regular and Chaotic Dynamics, vol.9, issue.2, pp.101-111, 2004. ,
Dynamics and statics of vortices on a plane and a sphere-i, Regular and Chaotic Dynamics, vol.3, issue.1, pp.28-38, 1998. ,
Tores invariants des systèemes hamiltoniens, 1985. ,
, , vol.639, pp.113-157
Choreographies in the n-vortex problem, Regular and Chaotic Dynamics, vol.23, issue.5, pp.595-612, 2018. ,
Lyapunov orbits in the n-vortex problem, Regular and Chaotic Dynamics, vol.19, issue.3, pp.348-362, 2014. ,
The four positive vortices problem: regions of chaotic behavior and the non-integrability, Annales de l'IHP Physique théorique, vol.59, pp.99-115, 1993. ,
A remark on the kam theorem applied to a four-vortex system, Journal of statistical physics, vol.52, issue.1-2, pp.471-477, 1988. ,
On chenciner-montgomery's orbit in the three-body problem, Discrete and Continuous Dynamical Systems, vol.7, issue.1, pp.85-90, 2001. ,
Action minimizing solutions of the newtonian n-body problem: from homology to symmetry, Proceedings of the ICM, vol.3, pp.255-264, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00145797
Unchained polygons and the n-body problem, Regular and chaotic dynamics, vol.14, issue.1, pp.64-115, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00292885
Simple choreographic motions of n bodies: a preliminary study, Geometry, mechanics, and dynamics, pp.287-308, 2002. ,
A remarkable periodic solution of the three-body problem in the case of equal masses, Annals of Mathematics-Second Series, vol.152, issue.3, pp.881-902, 2000. ,
The discrete nonlinear schrödinger equation-20 years on, Localization and energy transfer in nonlinear systems, pp.44-67, 2003. ,
Hamiltonian trajectories having prescribed minimal period, Communications on Pure and Applied Mathematics, vol.33, issue.2, pp.103-116, 1980. ,
Periodic solutions of n-vortex type hamiltonian systems near the domain boundary, SIAM Journal on Applied Mathematics, vol.78, issue.2, pp.977-995, 2018. ,
Periodic solutions of dynamical systems with newtonian type potentials, Periodic solutions of Hamiltonian systems and related topics, pp.111-115, 1987. ,
Periodic solutions with prescribed minimal period for convex autonomous hamiltonian systems, Inventiones mathematicae, vol.81, issue.1, pp.155-188, 1985. ,
, Convex analysis and variational problems, p.28, 1999.
Introduction to kam theory, with a view to celestial mechanics, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01422181
Rotating trapped bose-einstein condensates, Reviews of Modern Physics, vol.81, issue.2, p.647, 2009. ,
The weinstein conjecture in P ? C l, Mathematische Zeitschrift, vol.203, issue.1, pp.469-482, 1990. ,
A minimizing property of keplerian orbits, American Journal of Mathematics, pp.961-971, 1977. ,
Specielle Probleme über die Bewegung geradliniger paralleler Wirbelfäden, Druck von Zürcher und Furrer, vol.8, 1877. ,
Pseudo holomorphic curves in symplectic manifolds, Inventiones mathematicae, vol.82, issue.2, pp.307-347, 1985. ,
Finiteness of relative equilibria of the four-body problem, Inventiones mathematicae, vol.163, issue.2, pp.289-312, 2006. ,
Finiteness of stationary configurations of the four-vortex problem, Transactions of the American Mathematical Society, vol.361, issue.3, pp.1317-1332, 2009. ,
The stability of motion of rectilinear vortices in ring formation, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol.11, issue.70, pp.617-633, 1931. ,
Uber integrale der hydrodynamischen gleichungen, welche den wirbelbewegungen entsprechen, crelles j, vol.55, p.25, 1858. ,
The weinstein conjecture in cotangent bundles and related results, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.15, issue.4, pp.411-445, 1988. ,
The weinstein conjecture in the presence of holomorphic spheres, Communications on pure and applied mathematics, vol.45, issue.5, pp.583-622, 1992. ,
Symplectic invariants and Hamiltonian dynamics, 2012. ,
Quasi-periodic motions of vortex systems, Physica D: Nonlinear Phenomena, vol.4, issue.2, pp.261-269, 1982. ,
Vorlesungen tiber Mathematische Physik, 1876. ,
Non-integrability of the 4-vortex system: Analytical proof, Communications in mathematical physics, vol.120, issue.4, pp.643-652, 1989. ,
On aref's vortex motions with a symmetry center, Physica D: Nonlinear Phenomena, vol.16, issue.1, pp.27-61, 1985. ,
Symmetric equilibria for the N-vortex problem, Journal of Fixed Point Theory and Applications, vol.17, issue.3, pp.597-624, 2015. ,
Equilibria for the N-vortex-problem in a general bounded domain, Journal of Mathematical Analysis and Applications, vol.433, issue.2, pp.1531-1560, 2016. ,
Relative periodic orbits in point vortex systems, Nonlinearity, vol.17, issue.6, 1989. ,
URL : https://hal.archives-ouvertes.fr/hal-00015290
Rotating n-gon/kn-gon vortex configurations, Journal of Nonlinear Science, vol.6, issue.5, pp.385-414, 1996. ,
Problème général de la stabilité du mouvement, Annales de la Faculté des sciences de Toulouse: Mathématiques, vol.9, pp.203-474, 1907. ,
,
On the motion of vortices in two dimensions. Number 5, 1943. ,
Canonical transformations and graph theory, Physics Letters A, vol.138, issue.6-7, pp.258-266, 1989. ,
Existence of kam tori in the phase space of lattice vortex systems, J. App. Math. and Phys, vol.41, issue.6-7, pp.227-244, 1990. ,
Index theory for symplectic paths with applications, vol.207, 2012. ,
How the method of minimization of action avoids singularities, Celestial Mechanics and Dynamical Astronomy, vol.83, issue.1-4, pp.325-353, 2002. ,
Reduction of symplectic manifolds with symmetry, Reports on mathematical physics, vol.5, issue.1, pp.121-130, 1974. ,
J-holomorphic curves and symplectic topology, vol.52, 2012. ,
Introduction to Hamiltonian dynamical systems and the N-body problem, vol.90, 2008. ,
On central configurations, Mathematische Zeitschrift, vol.205, issue.1, pp.499-517, 1990. ,
Linear stability analysis of some symmetrical classes of relative equilibria, Hamiltonian Dynamical Systems, pp.291-317, 1995. ,
Vortex dynamics on a cylinder, SIAM Journal on Applied Dynamical Systems, vol.2, issue.3, pp.417-430, 2003. ,
The n-body problem, the braid group, and action-minimizing periodic solutions, Nonlinearity, vol.11, issue.2, pp.363-376, 1998. ,
Braids in classical dynamics, Physical Review Letters, vol.70, issue.24, p.3675, 1993. ,
Integrability of dynamical systems through differential galois theory: a practical guide. Differential algebra, complex analysis and orthogonal polynomials, vol.509, pp.143-220, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00629721
Periodic orbits near an equilibrium and a theorem by alan weinstein, Communications on Pure and Applied Mathematics, vol.29, issue.6, pp.727-747, 1976. ,
Algebraic geometry. I, complex projective varieties, 1976. ,
Dynamics and statistics of a system of vortices, Zh. Eksp. Teor. Fiz, vol.68, p.2, 1975. ,
Stationary configurations of point vortices, Transactions of the American Mathematical Society, vol.302, issue.2, pp.383-425, 1987. ,
The principle of symmetric criticality, Communications in Mathematical Physics, vol.69, issue.1, pp.19-30, 1979. ,
Classifying relative equilibria. i. Bulletin of the, vol.79, pp.904-908, 1973. ,
Classifying relative equilibria, vol.81, pp.489-491, 1975. ,
Classifying relative equilibria. iii, Letters in Mathematical Physics, vol.1, issue.1, pp.71-73, 1975. ,
, Measure of degenerate relative equilibria. i. Annals of Mathematics, pp.421-429, 1976.
Relative equilibria of vortices in two dimensions, Proceedings of the National Academy of Sciences, vol.79, issue.2, pp.716-718, 1982. ,
Translation of (Helmholtz 1858): On integrals of the hydrodynamical equations, which express vortex-motion. The London, Edinburgh, and Dublin Philosophical Magazine, Journal of Science, vol.33, issue.226, pp.485-512, 1867. ,
Les nouvelles méthodes de la mécanique céleste, 1892. ,
Théorie des tourbillons: Leçons professées pendant le deuxième semestre 1891-92, vol.11, 1893. ,
Sur les solutions périodiques et le principe de moindre action, Comptes rendus de l'Académie des Sciences, vol.123, pp.915-918, 1896. ,
Periodic solutions of Hamiltonian systems, Communications on Pure and Applied Mathematics, vol.31, issue.2, pp.157-184, 1978. ,
Periodic solutions of large norm of hamiltonian systems, Journal of Differential Equations, vol.50, pp.33-48, 1983. ,
Periodic and heteroclinic orbits for a periodic hamiltonian system, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.6, pp.331-346, 1989. ,
Minimax methods in critical point theory with applications to differential equations. Number 65, 1986. ,
Stability of relative equilibria in the planar n-vortex problem, SIAM Journal on Applied Dynamical Systems, vol.12, issue.2, pp.1114-1134, 2013. ,
Morse theory and relative equilibria in the planar n-vortex problem. Archive for Rational Mechanics and Analysis, vol.228, pp.209-236, 2018. ,
Existence of infinitely many homoclinic orbits in hamiltonian systems, Mathematische Zeitschrift, vol.209, issue.1, pp.27-42, 1992. ,
Appendix to smale's paper: Diagonals and relative equilibria, Manifolds-Amsterdam, pp.199-201, 1970. ,
Lectures on celestial mechanics, 2012. ,
, Topology and mechanics. i. Inventiones mathematicae, vol.10, pp.305-331, 1970.
, Topology and mechanics. ii. Inventiones mathematicae, vol.11, pp.45-64, 1970.
Mathematical problems for the next century. The mathematical intelligencer, vol.20, pp.7-15, 1998. ,
An infinite dimensional version of sard's theorem, The Collected Papers of, vol.2, pp.529-534, 2000. ,
Periodic motions of vortices on surfaces with symmetry, Journal of Fluid Mechanics, vol.460, pp.83-92, 2002. ,
Variational methods, 2008. ,
On the motion of three vortices, Canadian J. Math, vol.1, pp.257-270, 1949. ,
A Treatise on the Motion of Vortex Rings: an essay to which the Adams prize was adjudged in 1882, 1883. ,
On vortex atoms. The London, Journal of Science, vol.34, issue.227, pp.15-24, 1867. ,
On vortex motion, Earth and Environmental Science Transactions of the Royal Society of Edinburgh, vol.25, issue.1, pp.217-260, 1868. ,
Vortex statics, Proceedings of the Royal Society of Edinburgh, vol.9, pp.59-73, 1878. ,
Tourbillons dansants, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, vol.333, issue.10, pp.943-946, 2001. ,
Une caractérisation variationnelle des solutions de lagrange du probleme plan des trois corps, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, vol.332, issue.7, pp.641-644, 2001. ,
A proof of weinstein's conjecture in R 2n, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.4, pp.337-356, 1987. ,
, Capacités symplectiques et applications. Séminaire Bourbaki, p.31, 1988.
Relative periodic solutions of the n-vortex problem via the variational method. Archive for Rational Mechanics and Analysis, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01976971
Normal modes for nonlinear hamiltonian systems, Inventiones mathematicae, vol.20, issue.1, pp.47-57, 1973. ,
Periodic orbits for convex hamiltonian systems, Annals of Mathematics, vol.108, issue.3, pp.507-518, 1978. ,
On the hypotheses of rabinowitz'periodic orbit theorems, Journal of differential equations, vol.33, issue.3, pp.353-358, 1979. ,
Simple choreographies of the planar newtonian n-body problem. Archive for Rational Mechanics and, Analysis, vol.225, issue.2, pp.901-935, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-02262450
Periodic solutions for n-body type problems, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.7, pp.477-492, 1990. ,
A variational approach to homolinic orbits in hamiltonian systems, Mathematische Annalen, vol.288, issue.1, pp.133-160, 1990. ,
Nonintegrability of a problem on the motion of four point vortices, In Sov. Math. Dokl, vol.21, pp.296-299, 1980. ,