Wyniki wyszukiwania

1

Periodic segments and Nielsen numbers

100%

Wójcik K.

Banach Center Publications

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1999

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tom 47

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nr 1

247-252

EN

We prove that the Poincaré map $φ_{(0,T)}$ has at least $N(\tilde h, cl(W_{0} \ W_{0}^{-}) )$ fixed points (whose trajectories are contained inside the segment W) where the homeomorphism $\tilde h$ is given by the segment W.

2

Chaos in some planar nonautonomous polynomial differential equation

100%

Wójcik K.

Annales Polonici Mathematici

|

2000

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tom 73

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nr 2

159-168

EN

We show that under some assumptions on the function f the system $ż = z̅(f(z) e^{iϕt} + e^{i2ϕt})$ generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.

3

An attraction result and an index theorem for continuous flows on $ℝ^n × [0,∞)$

100%

Wójcik K.

Annales Polonici Mathematici

|

1996-1997

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tom 65

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nr 3

203-211

EN

We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on $E = ℝ^{n+1}$ for which $∂E = ℝ^n × {0}$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in E\∂E such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^n × [0,∞)$.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Banach Center Publications

3 Wójcik K.

1 2000

1 1999

1 1997

Periodic segments and Nielsen numbers

Chaos in some planar nonautonomous polynomial differential equation

An attraction result and an index theorem for continuous flows on $ℝ^n × [0,∞)$