Global dynamics of a planar mapping exhibiting orbits of periods 1, 2, 3 and no chaos
Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
◽
1990 ◽
Vol 333
(1630)
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pp. 209-259
Keyword(s):
A geometrical analysis of the planar mapping A : ( x,y ) -> ( y+xy,x ) is presented. A complete global portrait of the invariant manifolds of A is found, primarily by deductive methods. The behaviour of some manifolds was initially investigated numerically, but theoretical explanations for the observations are given in every case. The most significant features of the mapping A are : that it has periodic points of periods 1, 2 and 3 only; that it possesses no chaotic behaviour; that it has sequences of abutting regions of self-similar structure, and that it exhibits heteroclinic behaviour manifesting itself as exponentially small oscillations in some of the invariant manifolds.
2018 ◽
Vol 20
(4)
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pp. 408-418
2014 ◽
Vol 24
(06)
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pp. 1430017
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Keyword(s):
2020 ◽
Vol 66
(2)
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pp. 160-181
2014 ◽
Vol 24
(08)
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pp. 1440011
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1990 ◽
Vol 10
(2)
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pp. 295-318
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Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
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1992 ◽
Vol 338
(1651)
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pp. 557-568
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1996 ◽
Vol 06
(08)
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pp. 1529-1546
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2004 ◽
Vol 167
(792)
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pp. 0-0
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