Quanto segue è il testo della conferenza plenaria che ho tenuto al XVIII Congresso dell'Unione Matematica Italiana, in cui ho esposto il contenuto di due lavori in collaborazione con V. Barutello e G. Verzini ([2, 3]). In tali lavori si è sviluppato l'approccio variazionale alle traiettorie paraboliche della Meccanica Celeste, che connettono due configurazioni centrali minimali.
@article{BUMI_2012_9_5_3_689_0, author = {Susanna Terracini}, title = {Le traiettorie paraboliche della meccanica celeste come transizioni di fase minimali}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {5}, year = {2012}, pages = {689-710}, zbl = {1282.70029}, mrnumber = {3051740}, language = {it}, url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_3_689_0} }
Terracini, Susanna. Le traiettorie paraboliche della meccanica celeste come transizioni di fase minimali. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 689-710. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_3_689_0/
[1] On the singularities of generalized solutions to n-body-type problems, Int. Math. Res. Not. IMRN (2008). | MR 2439573 | Zbl 1143.70005
- - ,[2] Entire Minimal Parabolic Trajectories: the planar anisotropic Kepler problem, Arch. Ration. Mech. Anal., to appear (2011). | MR 3005324 | Zbl 1320.70006
- - ,[3] Entire Parabolic Trajectories as Minimal Phase Transitions, preprint (2011). | MR 3148122 | Zbl 1287.70007
- - ,[4] Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 401-412. | MR 779876 | Zbl 0588.35007
,[5] Sur certaines trajectoires du problème des n corps, Bulletin Astronomique, 35 (1918), 321-389.
,[6] Sur l'allure du mouvement dans le problème de trois corps quand le temps crois indèfinimment, Ann. Sci. Ec. Norm. Sup., 39 (1922), 29-130. | MR 1509241 | Zbl 48.1074.04
,[7] Action-minimizing orbits in the parallelogram four-body problem with equal masses, Arch. Ration. Mech. Anal., 158 (2001), 293-318. | MR 1847429 | Zbl 1028.70009
,[8] Existence and minimizing properties of retrograde orbits to the three-body problem with various choices of masses, Ann. of Math. (2), 167 (2008), 325-348. | MR 2415377 | Zbl 1170.70006
,[9] Variational constructions for some satellite orbits in periodic gravitational force fields, Amer. J. Math., 132 (2010), 681-709. | MR 2666904 | Zbl 1250.70012
,[10] Collisions totales, mouvements complètement paraboliques et réduction des homothéties dans le problème des n corps, Regul. Chaotic Dyn., 3 (1998), 93-106. | MR 1704972 | Zbl 0973.70011
,[11] A remarkable periodic solution of the three-body problem in the case of equal masses, Ann. of Math. (2), 152 (2000). | MR 1815704 | Zbl 0987.70009
- ,[12] The planetary N-body problem: Symplectic foliation, reductions and invariant tori, Invent. Math. (2011). | MR 2836051 | Zbl 1316.70010
- ,[13] Regularity properties of solutions to the basic problem in the calculus of variations, Trans. Amer. Math. Soc., 289 (1985), 73-98. | MR 779053 | Zbl 0563.49009
- ,[14] On the free time minimizers of the newtonian n-body problem, Math. Proc. Cambridge Philos. Soc., to appear (2011). | MR 3177865 | Zbl 1331.70035
- ,[15] Collision orbits in the anisotropic Kepler problem, Invent. Math., 45 (1978), 221-251. | MR 495360 | Zbl 0382.58015
,[16] Singularities in classical mechanical systems, in Ergodic theory and dynamical systems, I (College Park, Md., 1979-80), vol. 10 of Progr. Math., Birkhäuser Boston, Mass., 1981, 211-333. | MR 633766
,[17]
, Weak Kam Theorem in Lagrangian Dynamics, Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2007.[18] Weak KAM theorem on non compact manifolds, NoDEA Nonlinear Differential Equations Appl., 14 (2007), 1-27. | MR 2346451
- ,[19] 155 (2004), 363-388. | MR 2031431 | Zbl 1061.58008
- , Existence of critical subsolutions of the Hamilton-Jacobi equation, Invent. Math.,[20] Symmetry groups and non-planar collisionless action-minimizing solutions of the three-body problem in three-dimensional space, Arch. Ration. Mech. Anal., 179 (2006), 389-412. | MR 2208321 | Zbl 1138.70322
,[21] Transitive decomposition of symmetry groups for the n-body problem, Adv. Math., 213 (2007), 763-784. | MR 2332609 | Zbl 1114.70013
,[22] On the dihedral n-body problem, Nonlinearity, 21 (2008), 1307-1321. | MR 2422381 | Zbl 1138.70007
- ,[23] On the existence of collisionless equivariant minimizers for the classical n-body problem, Invent. Math., 155 (2004), 305-362. | MR 2031430 | Zbl 1068.70013
- ,[24] Platonic polyhedra, topological constraints and periodic solutions of the classical N-body problem, Invent. Math., 185 (2011), 283-332. | MR 2819162 | Zbl 1305.70023
- - ,[25] Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc., 204 (1975), 113-135. | MR 377983 | Zbl 0276.58005
,[26] A minimizing property of Keplerian orbits, Amer. J. Math., 99 (1977), 961-971. | MR 502484 | Zbl 0378.58006
,[27] The anisotropic Kepler problem in two dimensions, J. Mathematical Phys., 14 (1973), 139-152. | MR 349203
,[28] Bernoulli sequences and trajectories in the anisotropic Kepler problem, J. Mathematical Phys., 18 (1977), 806-823. | MR 459107
,[29] 3 of Texts in Applied Mathematics, Springer-Verlag, New York, 1991. | MR 1138981
- , Dynamics and bifurcations, vol.[30] On the manifolds of total collapse orbits and of completely parabolic orbits for the n-body problem, J. Differential Equations, 41 (1981), 27-43. | MR 626619 | Zbl 0475.70010
- ,[31] | MR 3752660 | Zbl 0783.70001
- , Classical planar scattering by coulombic potentials, Lecture Notes in Physics Monographs, Springer-Verlag, Berlin, 1992.[32] The n-centre problem of celestial mechanics for large energies, J. Eur. Math. Soc. (JEMS), 4 (2002), 1-114. | MR 1891507 | Zbl 1010.70011
,[33] Sur la régularisation du problème des trois corps, Acta Math., 42 (1920), 99-144. | MR 1555161 | Zbl 47.0837.01
,[34] Globally minimizing parabolic motions in the Newtonian N-body problem, Arch. Ration. Mech. Anal., 194 (2009), 283-313. | MR 2533929 | Zbl 1253.70015
- ,[35] On weak kam theory for N-body problems, Ergod. Th. & Dynam. Sys., to appear (2011). | MR 2995654
,[36] How the method of minimization of action avoids singularities, Celestial Mech. Dynam. Astronom., 83 (2002), 325-353. | MR 1956531 | Zbl 1073.70011
,[37] On the final evolution of the n-body problem, J. Differential Equations, 20 (1976), 150-186. | MR 416150 | Zbl 0336.70010
- ,[38] Triple collision in the collinear three-body problem, Invent. Math., 27 (1974), 191-227. | MR 359459 | Zbl 0297.70011
,[39] Chaotic dynamics near triple collision, Arch. Rational Mech. Anal., 107 (1989), 37-69. | MR 1000223 | Zbl 0697.70021
,[40] Braids in Classical Dynamics, Phys. Rev. Lett., 70, no. 24 (1993), 3675-3679. | MR 1220207 | Zbl 1050.37522
,[41] Regularization of Kepler's problem and the averaging method on a manifold, Comm. Pure. Appl. Math., 23 (1970), 609-636. | MR 269931 | Zbl 0193.53803
,[42] The behavior of gravitational systems, J. Math. Mech., 17 (1967/1968), 601-611. | MR 261826 | Zbl 0159.26102
,[43] | MR 434057 | Zbl 0353.70009
, Celestial mechanics, Mathematical Association of America, Washington, D. C., 1976.[44] Expanding gravitational systems, Trans. Amer. Math. Soc., 156 (1971), 219-240. | MR 275729 | Zbl 0215.57001
,[45] The manifold structure for collision and for hyperbolic-parabolic orbits in the n-body problem, J. Differential Equations, 55 (1984), 300-329. | MR 766126 | Zbl 0571.70009
,[46] Multiple symmetric periodic solutions to the 2n-body problem with equal masses, Nonlinearity, 19 (2006), 2441-2453. | MR 2260271 | Zbl 1260.70006
,[47] Minimizing periodic orbits with regularizable collisions in the n-body problem, Arch. Ration. Mech. Anal., 199 (2011), 821-841. | MR 2771668 | Zbl 1291.70049
,[48] Symmetric trajectories for the 2N-body problem with equal masses, Arch. Ration. Mech. Anal., 184 (2007), 465-493. | MR 2299759 | Zbl 1111.70010
- ,[49] Une caractérisation variationelle des solutions de Lagrange du problème plan des trois corps, Comp. Rend. Acad. Sci. Paris, 332, Série I (2001), 641-644. | MR 1841900 | Zbl 1034.70007
,[50] | MR 103613
, A treatise on the analytical dynamics of particles and rigid bodies: With an introduction to the problem of three bodies, 4th ed, Cambridge University Press (New York, 1959), xiv+456.[51] Quaternions for regularizing celestial mechanics: the right way, Celestial Mech. Dynam. Astronom., 102 (2008), 149-162. | MR 2452904 | Zbl 1154.70309
,