×

zbMATH — the first resource for mathematics

Sensitive dependence to initial conditions for one dimensional maps. (English) Zbl 0429.58012

MSC:
37E05 Dynamical systems involving maps of the interval
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Allwright, D.: Hypergraphic functions and bifurcation in recurrence relations. SIAM J. Appl. Math.34, 687–691 (1978) · Zbl 0381.92013
[2] Block, L., Franke, J.: Existence of periodic points for maps ofS 1. Inventiones Math.22, 69–73 (1973) · Zbl 0272.58005
[3] Bowen, R.: Invariant measures for Markov maps of the interval. Mimeographed, Berkeley 1978 · Zbl 0417.58011
[4] Cartan, E.: Leçons sur la théorie des espaces à connexions projective. Cahiers Scientifiques, Fascicule XVII. Paris: Gauthier-Villar 1937
[5] Denjoy, A.: Sur les courbes définies par les équations différentielles à la surface du tore. J. Math. Pures Appl.9, 333–375 (1932) · JFM 58.1124.04
[6] Guckenheimer, J.: On the bifurcation of maps of the interval. Inventiones Math.39, 165–178 (1977) · Zbl 0354.58013
[7] Guckenheimer, J.: Bifurcations of dynamical systems. C.I.M.E. Lectures, 1978 · Zbl 0451.58025
[8] Guckenheimer, J., Oster, G., Ipaktchi, A.: Dynamics of density dependent population models. J. Math. Biol.4, 101–147 (1977) · Zbl 0379.92016
[9] Hénon, M.: A two dimensional mapping with a strange attractor. Commun. Math. Phys.50, 69–77 (1976) · Zbl 0576.58018
[10] Herman, M.: Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Thesis, Orsay 1976 · Zbl 0347.58010
[11] Holmes, P., Moon, F.: A magnetoelastic strange attractor. Preprint, Cornell 1979 · Zbl 0405.73082
[12] Jakobson, M.: On smooth mappings of the circle into itself. Math. USSR sb.14, 161–185 (1971) · Zbl 0241.58006
[13] Jakobson, M.: Topological and metric properties of one dimensional endomorphisms. Doklady Akademia Nauk USSR243, 866–869 (1978)
[14] Jonker, L., Rand, D.: A lower bound for the entropy of certain maps of the unit interval. Preprint, Warwick 1978
[15] Jonker, L., Rand, D.: Bifurcations in one dimension. I, II. Preprint, Warwick 1979 · Zbl 0502.58025
[16] Lorenz, E.: Deterministic non periodic flow. J. Atmos. Sci20, 130–141 (1963) · Zbl 1417.37129
[17] Milnor, J., Thurston, W.: On iterated maps of the interval. I, II. Preprint, Princeton 1977 · Zbl 0393.57002
[18] Misiurewicz, M.: Structure of mappings of the interval with zero entropy. Preprint, I.H.E.S. 1978 · Zbl 0376.54019
[19] Misiurewicz, M., Szlenk, W.: Entropy of piecewise monotone mappings. Asterisque50, 299–310 (1977) · Zbl 0376.54019
[20] Parry, W.: Symbolic dynamics and transformations of the unit interval. Trans. Am. Math. Soc.122, 368–378 (1966) · Zbl 0146.18604
[21] Ruelle, D.: Sensitive dependence on initial conditions and turbulent behaviour of dynamical systems. Ann. N.Y. Acad. Sci. (to appear) · Zbl 0438.58003
[22] Ruelle, D.: On measures which describe turbulence. Preprint, I.H.E.S. 1979
[23] Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys.20, 167–192 (1971);23, 343 (1971) · Zbl 0223.76041
[24] Shaw, R.: Strange attractors, chaotic behavior, and information flow. Preprint, Santa-Cruz (1978)
[25] Singer, D.: Stable orbits and bifurcations of maps of the interval. SIAM J. Appl. Math.35, 260–267 (1978) · Zbl 0391.58014
[26] Spiegel, E., Marzec, C.: A strange attractor. Preprint, 1978 · Zbl 0471.65052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.