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Homoclinic points of mappings of the interval. (English) Zbl 0365.58015

MSC:
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
54H20 Topological dynamics (MSC2010)
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References:
[1] Louis Block, Continuous maps of the interval with finite nonwandering set, Trans. Amer. Math. Soc. 240 (1978), 221 – 230. · Zbl 0389.54006
[2] Louis Block, Mappings of the interval with finitely many periodic points have zero entropy, Proc. Amer. Math. Soc. 67 (1977), no. 2, 357 – 360. · Zbl 0344.54030
[3] Rufus Bowen and John Franks, The periodic points of maps of the disk and the interval, Topology 15 (1976), no. 4, 337 – 342. · Zbl 0346.58010
[4] O. M. Šarkovs\(^{\prime}\)kiĭ, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Mat. Ž. 16 (1964), 61 – 71 (Russian, with English summary).
[5] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747 – 817. · Zbl 0202.55202
[6] P. Štefan, A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), no. 3, 237 – 248.
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