Flexible periodic points
2014 ◽
Vol 35
(5)
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pp. 1394-1422
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Keyword(s):
We define the notion of ${\it\varepsilon}$-flexible periodic point: it is a periodic point with stable index equal to two whose dynamics restricted to the stable direction admits ${\it\varepsilon}$-perturbations both to a homothety and a saddle having an eigenvalue equal to one. We show that an ${\it\varepsilon}$-perturbation to an ${\it\varepsilon}$-flexible point allows us to change it to a stable index one periodic point whose (one-dimensional) stable manifold is an arbitrarily chosen $C^{1}$-curve. We also show that the existence of flexible points is a general phenomenon among systems with a robustly non-hyperbolic two-dimensional center-stable bundle.
1999 ◽
Vol 19
(5)
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pp. 1365-1378
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Keyword(s):
1966 ◽
Vol 25
◽
pp. 46-48
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2014 ◽
Vol 12
(6)
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pp. 485-506
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Keyword(s):
1982 ◽
Vol 14
(1-2)
◽
pp. 241-261
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Keyword(s):
2010 ◽
Vol 7
◽
pp. 90-97
Keyword(s):