Examples of expanding maps with some special properties
1987 ◽
Vol 36
(3)
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pp. 469-474
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Keyword(s):
The Real
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Let I be the unit interval [0, 1] of the real line. For integers k ≥ 1 and n ≥ 2, we construct simple piecewise monotonic expanding maps Fk, n in C0 (I, I) with the following three properties: (1) The positive integer n is an expanding constant for Fk, n for all k; (2) The topological entropy of Fk, n is greater than or equal to log n for all k; (3) Fk, n has periodic points of least period 2k · 3, but no periodic point of least period 2k−1 (2m+1) for any positive integer m. This is in contrast to the fact that there are expanding (but not piecewise monotonic) maps in C0(I, I) with very large expanding constants which have exactly one fixed point, say, at x = 1, but no other periodic point.
Keyword(s):
1969 ◽
Vol 16
(3)
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pp. 205-214
1998 ◽
Vol 21
(2)
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pp. 269-276
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1988 ◽
Vol 38
(1)
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pp. 125-130
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Keyword(s):
2005 ◽
Vol 153
(5-6)
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pp. 735-746
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