Keywords
- Periodic Orbit
- Periodic Point
- Finite Type
- Topological Entropy
- Homoclinic Tangency
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References
R. Bowen, On axiom A diffeomorphisms, Regional conference series in mathematics, no. 35, AMS.
P. Brunovsky, On one-parameter families of diffeomorphisms, Comment. Math. University Carolinae, 11 (1970), pp. 559–582.
P. Collet & J.P. Eckmann Iterated maps on the interval as dynamical systems, Birkhäuser, Boston, 1980.
J. Guckenheimer, Sensitive dependence to initial conditions for one dimensional maps, preprint IHES (1979).
M. Hénon, A two-dimensional mapping with a strange attractor, Comm. Math. Phys. 50, (1976), pp. 69–78.
B.R. Henry Escape from the unit interval under the transformation x→ψ.x.(1-x). Proc. Am. Math. Soc., 41, (1973), pp. 146–150.
M. Hirsch & C. Pugh, Stable manifolds and hyperbolic sets, Proc. Symp. in Pure Math., Vol. 14, AMS, Providence, R.I. (1970), pp. 133–164.
M. Hirsch, C. Pugh & M. Shub, Invariant manifolds, Lecture Notes in Math, 583, Springer Verlag, (1977).
L. Jonker, Periodic orbits and kneading invariants, Proc. London Math. Soc. 39 (1979), pp. 428–450.
L. Jonker & D.A. Rand, Bifurcations in one dimension, I: The nonwandering set; II: A versal model for bifurcations, Warwick Preprint, 1978. To appear in Inventiones Math.
J. Milnor, The theory of kneading, (Handwritten Notes), (1976).
J. Milnor & W. Thurston, On interated maps of the interval I and II, Preprint Princeton University & the Institute for Advanced Study, Princeton, (1977).
M. Misiurewicz, Structure of mappings of an interval with zero entropy, Preprint IHES, (1978).
M. Misiurewicz, Absolutely continuous measures for certains Markov maps of an interval, Preprint IHES, (1979).
S. Newhouse, The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms, Publ. Math. IHES, 50, (1979), pp. 101–152.
S. Newhouse, J. Palis & F. Takens, Stable arcs of diffeomorphisms, Bull. Am. Math. Soc., 82, (1976) and to appear.
L. Nusse, No chance to get lost, Preprint Utrecht, The Netherlands, unpublished.
D. Singer, Stable orbits and bifurcations of maps of the interval, SIAM, Journal of Appl. Math., 35, (1978), pp. 260–267.
S. Smale, Differentiable dynamical systems, Bull. Am. Math. Soc., 73, (1967), pp. 747–817.
J. Sotomayor, Genetic bifurcations of dynamical systems, Proc. of Symp. at Salvador, Academic Press, New York, (1973), pp. 561–582.
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© 1981 Springer-Verlag
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van Strien, S.J. (1981). On the bifurcations creating horseshoes. 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/BFb0091922
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DOI: https://doi.org/10.1007/BFb0091922
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