Proceedings of the Japan Academy, Series A, Mathematical Sciences

The existence of an invariant stable foliation and the problem of reducing to a one-dimensional map

Michiko Yuri

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 59, Number 4 (1983), 126-129.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195515631

Digital Object Identifier
doi:10.3792/pjaa.59.126

Mathematical Reviews number (MathSciNet)
MR711315

Zentralblatt MATH identifier
0522.58039

Subjects
Primary: 58F12
Secondary: 34C35

Citation

Yuri, Michiko. The existence of an invariant stable foliation and the problem of reducing to a one-dimensional map. Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 4, 126--129. doi:10.3792/pjaa.59.126. https://projecteuclid.org/euclid.pja/1195515631


Export citation

References

  • [1] E.N. Lorenz: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141 (1963).
  • [2] I. Shimada and T. Nagashima: On the C-system-like property of the Lorenz system. Progr. Theor. Phys., 58, 1318-1319 (1978).
  • [3] E. Rossler: An Equation for continuous chaos. Phys. Lett., 57A, 397- 398 (1976).
  • [4] R. M. May: Simple mathematical models with very complicated dynamics. Nature, 261, 459-467 (1976).
  • [5] J. Guckenheimer, G. Oster, and A. Ipaktchi: The dynamics of density dependent population models. J. Math. Biol., 4, 101-147 (1977).
  • [6] R. Shaw: Strange attractors. Chaotic behavior and information flow. Z. Naturforsch., 36a, 80-112 (1981).
  • [7] D. Ruelle: Ergodic theory of differentiate dynamical system. Publ. Math. Inst. HES, 50, 27-58 (1981).
  • [8] Ya. B. Pesin: Lyapunov characteristic exponents and smooth ergodic theory. Uspehi Mat. Nauk, 32, n4 (196), 55-112 (1977).
  • [9] V. I. Oseledec: A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical system. Trudy Mosk. Mat. Obsc, 19, 179-231 (1968).
  • [10] M. Yuri: A construction of an invariant stable foliation by the shadowing lemma. Tokyo Journal of Math, (preprint).