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Snap-back repellers imply chaos in $\bbfR^n$. (English) Zbl 0381.58004

37C70Attractors and repellers, topological structure
54H20Topological dynamics
92D25Population dynamics (general)
Full Text: DOI
[1] Li, T. -Y; Yorke, J. A.: Period three implies chaos. Amer. math. Monthly 82, 985-992 (1975) · Zbl 0351.92021
[2] Lorenz, E. N.: Deterministic nonperiodic flow. J. atmos. Sci. 20, 130-141 (1963)
[3] R. M. May, Mathematical aspects of the dynamics of animal populations, to appear.
[4] May, R. M.: Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186, 645-647 (1974)
[5] J. Guckenheimer, G. Oster, and A. Ipaktchi, The dynamics of density dependent population models, to appear. · Zbl 0379.92016
[6] Beddington, J. R.; Free, C. A.; Lawton, J. H.: Dynamic complexity in predator prey models framed in difference equations. Nature 255, 58-60 (1975)
[7] Smale, S.: Differentiable dynamical systems. Bull. amer. Math. soc. 73, 747-817 (1967) · Zbl 0202.55202
[8] F. R. Marotto, Doctoral Thesis, Boston University, Boston, Mass.