Periodic orbits of difference equations
1995 ◽
Vol 125
(4)
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pp. 657-674
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Keyword(s):
The Real
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The real difference equationan+2− (λ|an+1| + μan+1) +an= 0 may be interpreted as a dynamical system Φ:(an,an+1) ↦ (an+1,an+2) acting in the plane. The set ΛPof points (λ, μ) for which the mapping Φ is periodic has a rich structure. In this paper, we derive some geometric properties of ΛP(for example, we show that it is unbounded and uncountable), and we derive criteria for Φ to be periodic. We also investigate when Φ is conjugate to a rotation of the plane, and we describe how the rotation numbers of the corresponding circle maps Φ/|Φ| are related to the structure of ΛP.
1976 ◽
Vol 15
(3)
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pp. 371-379
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2008 ◽
Vol 18
(01)
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pp. 203-217
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2008 ◽
Vol 144
(4)
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pp. 867-919
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Keyword(s):
2014 ◽
Vol 24
(06)
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pp. 1450077
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