This is a preview of subscription content, log in via an institution to check access.
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
D. Aeyels, Generic observability of differentiable systems, preprint, April 1980, Dept. of System Dynamics, State Univ. Gent.
R. Bowen, Entropy of group endomorphisms and homogeneous spaces, Trans. A.M.S., 153 (1971), 401–414.
R. Bowen, On Axiom A diffeomorphisms, Regional Conference Series in Mathematics, 35, A.M.S. Providence, 1977.
M. Denker, C. Grillenberger, & K. Sigmund, Ergodic theory on compact spaces, Lecture Notes in Mathematics, 527, Springer-Verlag, Berlin, 1976.
H. Federer, Geometric measure theory, Springer-Verlag, Berlin, 1969.
P.R. Fenstermacher, J.L. Swinney & J.P. Gollub, Dynamical instability and the transition to chaotic Taylor vortex flow, Journal Fluid Mech. 94 (1979) (1) 103–128.
P. Frederickson, J.L. Kaplan & J.A. Yorke, The dimension of the strange attractor for a class of difference systems, preprint, June 1980, University of Maryland.
J.P. Gollub, The onset of turbulence: convection, surface waves, and oscillations, in Systems far from Equilibrium, Proc. Sitges Int. School and Symposium on Statistical Mech., Ed. L. Garrido, J. Garcia, Lecture Notes in Physics, Springer-Verlag, Berlin, to appear.
J.P. Gollub, & S.V. Benson, Time-dependent instability and the transition to, turbulent convection, preprint, Physics Dept, Haverford College, Haverford, Pa. 19041, USA.
J.P. Gollub & H.L. Swinney, Onset of turbulence in a rotating fluid, Phys. Rev. Lett. 35 (1975), 927–930.
M. Herman, Mesure de Lebesgue et nombre de rotation, in Geometry and Topology, ed. J. Palis and M. do Carmo, Lecture Notes in Mathematics 597, Springer-Verlag, Berlin, 1977.
W. Hurewicz & H. Wallman, Dimension theory, Princeton University Press, 1948, Princeton, N.J.
L. Landau & E. Lifschitz, Méchanic des Fluides, ed. MIR, Moscow, 1971.
R. Mañé, On the dimension of the compact invariant sets of certain non-linear maps, preprint IMPA, Rio de Janeiro, 1980.
J.E. Marsden, The Hopf bifurcation for non-linear semi groups, Bull. A.M.S., 79 (1973), 537–541.
J.E. Marsden & M. McCracken, The Hopf bifurcation and its applications, Appl. math. sci. 19, Springer-Verlag, Berlin, 1976.
N.H. Packerd, J.P. Crutchfield, J.D. Farmer & R.S. Shaw, Geometry from the time series, preprint, May 1979, University of California, Santa Cruz, (Dynamical Systems Collective).
D. Rand, The pre-turbulent transitions and flows of a viscous fluid between concentric rotating cylinders, preprint Warwick University, June 1980.
D. Ruelle & F. Takens, On the nature of turbulence, Comm. math. Phys. 20 (1971), 167–192; 23 (1971), 343–344.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Takens, F. (1981). Detecting strange attractors in turbulence. In: Rand, D., Young, LS. (eds) Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics, vol 898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091924
Download citation
DOI: https://doi.org/10.1007/BFb0091924
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11171-9
Online ISBN: 978-3-540-38945-3
eBook Packages: Springer Book Archive