Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: Rigorous nonextensive solutions

Europhysics Letters

Volumn 60, Issue 4, 2002, Pages 518-524

  Baldovin, F ^a   Robledo, A ^b  

^a CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036853246     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2002-00249-7     Document Type: Article

References (22)

1. Tsallis C., J. Stat. Phys., 52 (1988) 479; Curado E.M.F. and Tsallis C., J. Phys. A, 24 (1991) L69 (Corrigenda: 24 (1991) 3187 and 25 (1992) 1019). A recent review can be found in Tsallis C., Nonextensive Statistical Mechanics and Its Applications, edited by Abe S. and Okamoto Y., Lect. Notes Phys., Vol. 560 (Springer, Berlin) 2001, p. 3. See http://tsallis.cat.cbpf.br/biblio.htm for full bibliography.
2. Tsallis C., J. Stat. Phys., 52 (1988) 479; Curado E.M.F. and Tsallis C., J. Phys. A, 24 (1991) L69 (Corrigenda: 24 (1991) 3187 and 25 (1992) 1019). A recent review can be found in Tsallis C., Nonextensive Statistical Mechanics and Its Applications, edited by Abe S. and Okamoto Y., Lect. Notes Phys., Vol. 560 (Springer, Berlin) 2001, p. 3. See http://tsallis.cat.cbpf.br/biblio.htm for full bibliography.
3. Tsallis C., J. Stat. Phys., 52 (1988) 479; Curado E.M.F. and Tsallis C., J. Phys. A, 24 (1991) L69 (Corrigenda: 24 (1991) 3187 and 25 (1992) 1019). A recent review can be found in Tsallis C., Nonextensive Statistical Mechanics and Its Applications, edited by Abe S. and Okamoto Y., Lect. Notes Phys., Vol. 560 (Springer, Berlin) 2001, p. 3. See http://tsallis.cat.cbpf.br/biblio.htm for full bibliography.
4. Tsallis C., Plastino A.R. and Zheng W.-M., Chaos, Solitons and Fractals, 8 (1997) 885. See also Grassberger P. and Scheunert M., J. Stat. Phys., 26 (1981) 697; schneider T., Politi A. and Wurtz D., Z. Phys. B, 66 (1987) 469; Anania G. and Politi A., Europhys. Lett., 7 (1988) 119; Hata H., Horita T. and Mori H., Prog. Theor. Phys., 82 (1989) 897.
5. Tsallis C., Plastino A.R. and Zheng W.-M., Chaos, Solitons and Fractals, 8 (1997) 885. See also Grassberger P. and Scheunert M., J. Stat. Phys., 26 (1981) 697; Schneider T., Politi A. and Wurtz D., Z. Phys. B, 66 (1987) 469; Anania G. and Politi A., Europhys. Lett., 7 (1988) 119; Hata H., Horita T. and Mori H., Prog. Theor. Phys., 82 (1989) 897.
6. Tsallis C., Plastino A.R. and Zheng W.-M., Chaos, Solitons and Fractals, 8 (1997) 885. See also Grassberger P. and Scheunert M., J. Stat. Phys., 26 (1981) 697; Schneider T., Politi A. and Wurtz D., Z. Phys. B, 66 (1987) 469; Anania G. and Politi A., Europhys. Lett., 7 (1988) 119; Hata H., Horita T. and Mori H., Prog. Theor. Phys., 82 (1989) 897.
7. Tsallis C., Plastino A.R. and Zheng W.-M., Chaos, Solitons and Fractals, 8 (1997) 885. See also Grassberger P. and Scheunert M., J. Stat. Phys., 26 (1981) 697; Schneider T., Politi A. and Wurtz D., Z. Phys. B, 66 (1987) 469; Anania G. and Politi A., Europhys. Lett., 7 (1988) 119; Hata H., Horita T. and Mori H., Prog. Theor. Phys., 82 (1989) 897.
8. Tsallis C., Plastino A.R. and Zheng W.-M., Chaos, Solitons and Fractals, 8 (1997) 885. See also Grassberger P. and Scheunert M., J. Stat. Phys., 26 (1981) 697; Schneider T., Politi A. and Wurtz D., Z. Phys. B, 66 (1987) 469; Anania G. and Politi A., Europhys. Lett., 7 (1988) 119; Hata H., Horita T. and Mori H., Prog. Theor. Phys., 82 (1989) 897.
9. Costa U.M.S., Lyra M.L., Plastino A.R. and Tsallis C., Phys. Rev. E, 56 (1997) 245.
10. Lyra M.L. and Tsallis C., Phys. Rev. Lett., 80 (1998) 53.
11. de Moura F.A.B.F., Tirnakli U. and Lyra M.L., Phys. Rev. E, 62 (2000) 6361.
12. Baldovin F., Tsallis C. and Schulze B., cond-mat/0203595.
13. See, e.g., Schuster H.G., Deterministic Chaos. An Introduction, 2nd revised edition (VHC Publishers, Weinheim) 1988; Ott E., Chaos in Dynamical Systems (Cambridge University Press, Cambridge) 1993.
14. See, e.g., Schuster H.G., Deterministic Chaos. An Introduction, 2nd revised edition (VHC Publishers, Weinheim) 1988; Ott E., Chaos in Dynamical Systems (Cambridge University Press, Cambridge) 1993.
15. Robledo A., cond-mat/0202095.
16. Beck C. and Schlogl F., Thermodynamics of Chaotic Systems: An Introduction (Cambridge University Press, Cambridge) 1993, p. 164ff.
17. Hu B. and Rudnick J., Phys. Rev. Lett., 48 (1982) 1645. See also Hirsch J.E., Nauenberg M. and Scalapino D.J., Phys. Lett. A, 87 (1982) 391.
18. Hu B. and Rudnick J., Phys. Rev. Lett., 48 (1982) 1645. See also Hirsch J.E., Nauenberg M. and Scalapino D.J., Phys. Lett. A, 87 (1982) 391.
19. Feigenbaum M., J. Stat. Phys., 19 (1978) 25; 21 (1979) 669.
20. Feigenbaum M., J. Stat. Phys., 19 (1978) 25; 21 (1979) 669.
21. Buiatti M., Grigolini P. and Montagnini A., Phys. Rev. Lett., 82 (1999) 3383.
22. Gaspard P. and Wang X.J., Proc. Natl. Acad. Sci. USA, 85 (1988) 4591.