Off to infinity in finite time

Donald G. Saari; Zhihong Xia

Pokroky matematiky, fyziky a astronomie (1997)

  • Volume: 42, Issue: 2, page 90-102
  • ISSN: 0032-2423

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Saari, Donald G., and Xia, Zhihong. "Do nekonečna v konečném čase." Pokroky matematiky, fyziky a astronomie 42.2 (1997): 90-102. <http://eudml.org/doc/37447>.

@article{Saari1997,
author = {Saari, Donald G., Xia, Zhihong},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {singularity; collision},
language = {cze},
number = {2},
pages = {90-102},
publisher = {Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists},
title = {Do nekonečna v konečném čase},
url = {http://eudml.org/doc/37447},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Saari, Donald G.
AU - Xia, Zhihong
TI - Do nekonečna v konečném čase
JO - Pokroky matematiky, fyziky a astronomie
PY - 1997
PB - Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists
VL - 42
IS - 2
SP - 90
EP - 102
LA - cze
KW - singularity; collision
UR - http://eudml.org/doc/37447
ER -

References

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  1. Anosov, D., Smooth dynamical systems. Introductory article, Amer. Math. Soc. Transl. 125 (1985), 1–20. (1985) Zbl0569.58025
  2. Chazy, J., Sur les singularités impossible du problème des n corps, C. R. Acad. Sci. Paris 170 (1920), 575–577. (1920) Zbl47.0845.04
  3. Devaney, R., Triple collisions in the planar isosceles three-body problem, Invent. Math. 60 (1980), 249–267. (1980) Zbl0438.58014MR0586428
  4. Devaney, R., Singularities in classical mechanical systems, Basel and Boston, MA, Birkhäuser 1981. (1981) Zbl0467.70016MR0633766
  5. Gerver, J., The existence of pseudocollisions in the plane, J. Differential Equations 89 (1991), 1–68. (1991) Zbl0721.70007MR1088334
  6. Littlewood, J., Some problems in real and complex analysis, Boston, MA, Heath 1969. (1969) Zbl0185.11502MR0244463
  7. McGehee, R., Von Zeipel’s theorem on singularities in celestial mechanics, Exposition. Math. 4 (1986), 335–345. (1986) Zbl0622.70005MR0867962
  8. McGehee, R., Triple collisions in the collinear three-body problem, Invent. Math. 29 (1974), 191–227. (1974) Zbl0297.70011MR0359459
  9. Mather, J., McGehee, R., Solutions of the collinear four-body problem which become unbounded in finite time, Lecture Notes Phys. 38 (1975), 573–597. (1975) Zbl0331.70005MR0495348
  10. Moekel, R., Orbits of the three-body problem which pass infinitely close to triple collision, Amer. J. Math. 
  11. Moekel, R., Heteroclinic phenomena in the isosceles three-body problem, SIAM J. Math. Anal. 15 (1984). (1984) MR0755848
  12. Marchal, C., Saari, D. G., On the final evolution of the n -body problem, J. Differential Equations 20 (1976), 150–186. (1976) Zbl0336.70010MR0416150
  13. Painlevé, P., Leçons sur la théorie analytic des équations différentielles, Paris, Hermann 1897. (1897) Zbl28.0262.01
  14. Pollard, H., A mathematical introduction to celestial mechanics, Carus Monograph No. 18, Math. Assoc. Amer. (1976). (1976) Zbl0141.23803MR0434057
  15. Pollard, H., Gravitational systems, J. Math. Mech. 17 (1967), 601–612. (1967) Zbl0159.26102MR0261826
  16. Pollard, H., Saari, D. G., Singularities of the n -body problem 1, Arch. Rational Mech. Math. 30 (1968), 263–269. (1968) Zbl0174.26904MR0231565
  17. Pollard, H., Saari, D. G., Singularities of the n -body problem 2, Academic Press 1970, 255–259. (1970) Zbl0228.70021MR0277853
  18. Robinson, C., Dynamical systems, Boca Raton, FL, CRC Press, Inc., 1995. (1995) Zbl0853.58001MR1396532
  19. Saari, D. G., Singularities of the Newtonian n -body problem, Ph. D. Dissertation, Purdue University 1967. (1967) 
  20. Saari, D. G., Improbability of collisions in Newtonian gravitational systems II, Trans. Amer. Math. Soc. 181 (1973), 351–368. (1973) Zbl0283.70007MR0321386
  21. Saari, D. G., Singularities and collisions of Newtonian gravitational systems, Arch. Rational Mech. Math. 49 (1973), 311–320. (1973) Zbl0253.70010MR0339596
  22. Saari, D. G., A global existence theorem for the four-body problem of Newtonian mechanics, J. Differential Equations 26 (1977), 80–111. (1977) Zbl0353.70008MR0478863
  23. Siegel, C. L., Der Dreierstoss, Ann. of Math. 42 (1941), 127–168. (1941) Zbl0024.36404MR0003736
  24. Simó, C., Analysis of triple-collision in the isosceles problem, New York, Marcel Dekker 1980. (1980) Zbl0478.70007MR0640127
  25. Sperling, H. J., On the real singularities of the n -body problem, J. Reine Angew. Math. 245 (1970), 15–40. (1970) Zbl0207.23301MR0290630
  26. Sundman, K., Le problème des trois corps, Acta Soc. Sci. Fenn. 35 (1909). (1909) Zbl40.1017.07
  27. Saari, D. G., Xia, Z., Oscillatory and superhyperbolic solutions in Newtonian systems, J. Differential Equations 82 (1989), 342–355. (1989) Zbl0705.34034MR1027973
  28. Zeipel, H. von, Sur les singularités du problème des n corps, Ark. Mat. Astronom. Fys. 4 (1904). (1904) 
  29. Wintner, A., The analytical foundations of celestial mechanics, Princeton, NJ, Princeton University Press 1947. (1947) Zbl0041.59006MR0005824
  30. Xia, Z., The existence of non-collision singularities in Newtonian systems, Ph. D. Dissertation, Northwestern University 1988. (1988) 
  31. Xia, Z., The existence of non-collision singularities in Newtonian systems, Ann. of Math. 135 (1992), 411–468. (1992) MR1166640

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