The Eisenhart geometry as an alternative description of dynamics in terms of geodesics

General Relativity and Gravitation

Volumn 30, Issue 6, 1998, Pages 887-914

  Szydlowski, Marek ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

Deterministic chaos; Particle trajectories

Indexed keywords

EID: 0032219714     PISSN: 00017701     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026612225777     Document Type: Article

References (53)

1. 1. Abramowicz, M. A., Carter, B., and Lasota, J. P. (1988). Gen. Rel. Grav. 20, 1173.
2. 2. Arnold, V. I., Kozlov, V. V., and Neishtadt, A. I. (1988). In Dynamical Systems III, V. I. Arnold, ed. (Springer-Verlag, Berlin).
3. 3. Arnowitt, R., Deser, S., and Misner, C. W. (1962). In Gravitation: An Introduction to Current Research, L. Witten, ed. (Wiley, New York).
4. 4. Blanco, S., Costa, A., and Rosso, O. A. (1995). Gen. Rel. Grav. 27, 1295.
5. 5. Bogoyavlenski, O. I. (1976). Commun. Math. Phys. 51, 201; Biesiada, M., and Szydlowski, M. (1991). Phys. Lett. A160, 123.
6. 5. Bogoyavlenski, O. I. (1976). Commun. Math. Phys. 51, 201; Biesiada, M., and Szydlowski, M. (1991). Phys. Lett. A160, 123.
7. 6. Bogoyavlenski, O. I., and Novikov, S. P. (1973). Sov. Phys. JETP 64, 1475.
8. 7. Calzetta, E., and El Hasi, C. (1993). Class. Quantum Grav. 10, 1825.
9. 8. Calzetta, E., and Gonzales, J. J. (1995). Phys. Rev. D51, 6821.
10. 9. Cornish, N. J., and Levin, J. J. (1996). Phys. Rev. D53, 3022.
11. 10. Dejonghe, H., and Hut, P. (1986). In The Use of Supercomputers in Stellar Dynamics, P. Hut and S. McMillan, eds. (Springer-Verlag, Berlin).
12. 11. de Witt, B. (1967). Phys. Rev. 160, 1113.
13. 12. Eisenhart, L. P. (1929). Ann. Math. 30, 591.
14. 13. Feinberg, J., and Peleg, V. (1995). Phys. Rev. D52, 1988.
15. 14. Goodman, J., Heggie, D. G., and Hut, P. (1992). Preprint IASSNS-ATS 92/16; Kandrup, H. E., and Smith, H. (1991). Astrophys. J. 374, 255; Kandrup, H. E., Mahon, E. M., and Smith, H. S. (1994). Astrophys. J. 428, 458; Kandrup, H. E. (1989). Phys. Lett. 4140, 97.
16. 14. Goodman, J., Heggie, D. G., and Hut, P. (1992). Preprint IASSNS-ATS 92/16; Kandrup, H. E., and Smith, H. (1991). Astrophys. J. 374, 255; Kandrup, H. E., Mahon, E. M., and Smith, H. S. (1994). Astrophys. J. 428, 458; Kandrup, H. E. (1989). Phys. Lett. 4140, 97.
17. 14. Goodman, J., Heggie, D. G., and Hut, P. (1992). Preprint IASSNS-ATS 92/16; Kandrup, H. E., and Smith, H. (1991). Astrophys. J. 374, 255; Kandrup, H. E., Mahon, E. M., and Smith, H. S. (1994). Astrophys. J. 428, 458; Kandrup, H. E. (1989). Phys. Lett. 4140, 97.
18. 14. Goodman, J., Heggie, D. G., and Hut, P. (1992). Preprint IASSNS-ATS 92/16; Kandrup, H. E., and Smith, H. (1991). Astrophys. J. 374, 255; Kandrup, H. E., Mahon, E. M., and Smith, H. S. (1994). Astrophys. J. 428, 458; Kandrup, H. E. (1989). Phys. Lett. A140, 97.
19. 15. Gurzadyan, V. G., and Savvidy, G. K. (1986). Astron. Astrophys. 160, 203.
20. 16. Hadamard, J. (1898). J. Math. Pure Appl. 27, 489; Arnold, V. I. (1978). Mathematical Methods of Classical Mechanics (Springer-Verlag, New York); Arnold, V. I., and Avez, A. (1968). Ergodic Problems of Classical Mechanics (Benjamin, New York).
21. 16. Hadamard, J. (1898). J. Math. Pure Appl. 27, 489; Arnold, V. I. (1978). Mathematical Methods of Classical Mechanics (Springer-Verlag, New York); Arnold, V. I., and Avez, A. (1968). Ergodic Problems of Classical Mechanics (Benjamin, New York).
22. 16. Hadamard, J. (1898). J. Math. Pure Appl. 27, 489; Arnold, V. I. (1978). Mathematical Methods of Classical Mechanics (Springer-Verlag, New York); Arnold, V. I., and Avez, A. (1968). Ergodic Problems of Classical Mechanics (Benjamin, New York).
23. 17. Hawking, S. W., and Luttrell, J. C. (1984). Nucl. Phys. B247, 250.
24. 18. Heggie, D. G. (1988). In Long-term Dynamical Behaviour and Artificial N-body Systems, A. E. Roy, ed. (Kluwer, Dordrecht).
25. 19. Heggie, D. G. (1991). In Predictability, Stability and Chaos in N-body Dynamical Systems, A. E. Roy, ed. (Plenum Press, New York).
26. 20. Kamenshchik, A. Xu., Khalatnikov, I. M., and Toporensky, A. V. (1996). Phys. Lett. B357, 36.
27. 21. Landau, L. D., and Lifshitz, E. M. (1971). The Classical Theory of Fields (Pergamon Press, Oxford).
28. 22. Miller, R. H. (1964). Astrophys. J. 140, 250.
29. 23. Misner, C. W. (1972). In Magic without Magic, J. Klauder, ed. (Freeman, San Francisco).
30. 24. Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation (W. H. Freeman, San Francisco).
31. 25. Pettini, M. (1993). Phys. Rev. E47, 826; Casetti, L., Livi, R., and Pettini, M. (1995). Phys. Rev. Lett. 74, 375; Casetti, L., Clementi, C., and Pettini, M. (1996). Phys. Rev. E54, 5969.
32. 25. Pettini, M. (1993). Phys. Rev. E47, 826; Casetti, L., Livi, R., and Pettini, M. (1995). Phys. Rev. Lett. 74, 375; Casetti, L., Clementi, C., and Pettini, M. (1996). Phys. Rev. E54, 5969.
33. 25. Pettini, M. (1993). Phys. Rev. E47, 826; Casetti, L., Livi, R., and Pettini, M. (1995). Phys. Rev. Lett. 74, 375; Casetti, L., Clementi, C., and Pettini, M. (1996). Phys. Rev. E54, 5969.
34. 26. Quinlan, G. D., and Tremaine, S. (1992). Mon. Not. R. Astr. Soc. 259, 505.
35. 27. Rabuszko, A. P. (1987). Problem of Stability of Motion of Body in General Relativity (Highschool, Minsk, in Russian).
36. 28. Schmidt, H.-J. (1996). J. Math. Phys. 37, 1244.
37. 29. Schutz, B. (1985). A First Course in General Relativity (Cambridge University Press, Cambridge).
38. 30. Shebehely, W. (1984). Cell. Mech. 34, 49.
39. 31. Sinai, Y. G. (1970). Russ. Math. Surv. 25, 137; Sinai, Y. G. (1970). Usp. Mat. Nauk 25, 141; Bunimovich, L. A., and Sinai, Y. G. (1973). Mat. Sb. 90, 415; Bunimovich, L. A., and Sinai, Y. G. (1973). Math. USSR Sb. 19, 407; Bunimovich, L. A. (1979). Commun. Math. Phys. 65, 295; Szasz, D. (1992). Commun. Math. Phys. 145, 595.
40. 31. Sinai, Y. G. (1970). Russ. Math. Surv. 25, 137; Sinai, Y. G. (1970). Usp. Mat. Nauk 25, 141; Bunimovich, L. A., and Sinai, Y. G. (1973). Mat. Sb. 90, 415; Bunimovich, L. A., and Sinai, Y. G. (1973). Math. USSR Sb. 19, 407; Bunimovich, L. A. (1979). Commun. Math. Phys. 65, 295; Szasz, D. (1992). Commun. Math. Phys. 145, 595.
41. 31. Sinai, Y. G. (1970). Russ. Math. Surv. 25, 137; Sinai, Y. G. (1970). Usp. Mat. Nauk 25, 141; Bunimovich, L. A., and Sinai, Y. G. (1973). Mat. Sb. 90, 415; Bunimovich, L. A., and Sinai, Y. G. (1973). Math. USSR Sb. 19, 407; Bunimovich, L. A. (1979). Commun. Math. Phys. 65, 295; Szasz, D. (1992). Commun. Math. Phys. 145, 595.
42. 31. Sinai, Y. G. (1970). Russ. Math. Surv. 25, 137; Sinai, Y. G. (1970). Usp. Mat. Nauk 25, 141; Bunimovich, L. A., and Sinai, Y. G. (1973). Mat. Sb. 90, 415; Bunimovich, L. A., and Sinai, Y. G. (1973). Math. USSR Sb. 19, 407; Bunimovich, L. A. (1979). Commun. Math. Phys. 65, 295; Szasz, D. (1992). Commun. Math. Phys. 145, 595.
43. 31. Sinai, Y. G. (1970). Russ. Math. Surv. 25, 137; Sinai, Y. G. (1970). Usp. Mat. Nauk 25, 141; Bunimovich, L. A., and Sinai, Y. G. (1973). Mat. Sb. 90, 415; Bunimovich, L. A., and Sinai, Y. G. (1973). Math. USSR Sb. 19, 407; Bunimovich, L. A. (1979). Commun. Math. Phys. 65, 295; Szasz, D. (1992). Commun. Math. Phys. 145, 595.
44. 31. Sinai, Y. G. (1970). Russ. Math. Surv. 25, 137; Sinai, Y. G. (1970). Usp. Mat. Nauk 25, 141; Bunimovich, L. A., and Sinai, Y. G. (1973). Mat. Sb. 90, 415; Bunimovich, L. A., and Sinai, Y. G. (1973). Math. USSR Sb. 19, 407; Bunimovich, L. A. (1979). Commun. Math. Phys. 65, 295; Szasz, D. (1992). Commun. Math. Phys. 145, 595.
45. 32. Standish, E. M. (1968). Ph. D. Thesis, Yale University.
46. 33. Szydlowski, M. (1994). J. Math. Phys. 35, 1850.
47. 34. Szydlowski, M. (1997). Contemporary Math. 203, 289.
48. 35. Szydlowski, M., Heller, M., and Sasin, W. (1996). J. Math. Phys. 37, 346.
49. 36. Szydlowski, M., and Krawiec, A. (1996). Phys. Rev. D53, 6893.
50. 37. Szydlowski, M., and Pajdosz, G. (1989). Class. Quantum Grav. 6, 1391.
51. 38. Szydlowski, M., and Szczesny, J. (1994). Phys. Rev. D50, 819.
52. 39. Thirring, W. (1977). Klassische Dynamische Systeme (Springer-Verlag, Wien, New York).
53. 40. Varvoglis, H., and Papadopoulos, D. (1992). Astron. Astrophys. 261, 664.