Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Bowen Bernoulli maps of the interval (To appear.)
J. Guckenheimer A strange, strange attractor. (To appear.)
A. O. Gelfond On a general property of number systems, Izv. Akad. Nauk. S.S.S.R. 23 (1959) 809–814
M. Hirsch and S. Smale Differential equations, dynamical systems and linear algebra. Acad.Press 1974 New York
S. Halfin Explicit construction of invariant measures for a class of continuous state Markov processes. Annals of Prob. (1975) 859–864.
Z.S. Kowalski Invariant measures for piecewise monotonic transformations. Springer Lecture Notes (472).
E.N. Lorenz Deterministic nonperiodic flow. Journal of the Atmos. Sc. 20 (1963) 130–141.
A. Lasota and Y. York. On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc. (1973) 481–488.
W. Parry Symbolic dynamics and transformations of the unit interval. Trans. Amer. Math. Soc. 122 (1966) 368–378.
W. Parry Representations for real numbers. Acta. Math. Acad. Sci. Hung. (1964), 95–105.
W. Parry On the β-expansions of real numbers. Acta. Math. Acad. Sci. Hung. (1960) 401–416.
D. Rand Kneading for the Lorenz attractor. Preprint, University of Warwick.
D. Ruelle and F. Takens On the nature of turbulence. Commun. Math. Phys. 20 (1971) 167–192.
P. Shields The theory of Bernoulli shifts. Chicago Lectures in Math. 1973
S. Smale and R.F. Williams The qualitative analysis of a difference equation of population growth. (To appear.)
R.F. Williams The structure of Lorenz attractors. (To appear).
K.M. Wilkinson Ergodic properties of a class of piecewise linear transformations. Z. Wahrscheinlichkeitstheorie verw. Gebiete. 31. (1975), 303–328.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Parry, W. (1979). The lorenz attractor and a related population model. In: Denker, M., Jacobs, K. (eds) Ergodic Theory. Lecture Notes in Mathematics, vol 729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063293
Download citation
DOI: https://doi.org/10.1007/BFb0063293
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09517-0
Online ISBN: 978-3-540-35130-6
eBook Packages: Springer Book Archive