Browsing by Author "Zgliczynski, Piotr"

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On stability of forcing relations for multidimensional perturbations of interval maps
(2009)
Li, Ming-Chia
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Zgliczynski, Piotr
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應用數學系
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Department of Applied Mathematics
We show that all periods of periodic points forced by a pattern for interval maps are preserved for high-dimensional maps if the multidimensional perturbation is small. We also show that if an interval map has a fixed point associated with a homoclinic-like orbit then any small multidimensional perturbation has periodic points of all periods.
Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps
(2008-11-01)
Li, Ming-Chia
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Lyu, Ming-Jiea
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Zgliczynski, Piotr
;
應用數學系
;
Department of Applied Mathematics
We consider a one-parameter family of maps F(lambda) on R(m) x R(n) with the singular map F(0) having one of the two forms (i) F(0) (x, y) = (f (x), g(x)), where f : R(m) -> R(m) and g : R(m) -> R(n) are continuous, and (ii) F(0)( x, y) = (f (x), g(x, y)), where f : R(m) -> R(m) and g : R(m) x R(n) -> Rn are continuous and g is locally trapping along the second variable y. We show that if f is one-dimensional and has a positive topological entropy, or if f is high-dimensional and has a snap-back repeller, then F. has a positive topological entropy for all lambda close enough to 0.