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On Existence of Positive Periodic Solutions.

Klaudiusz Wójcik — 1998

Monatshefte für Mathematik

An attraction result and an index theorem for continuous flows on $ℝ^{n} \times [0, \infty)$

Klaudiusz Wójcik — 1997

Annales Polonici Mathematici

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 $\partial E = ℝ^{n} \times 0$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^{n} \times [0, \infty)$ .

Chaos in some planar nonautonomous polynomial differential equation

Klaudiusz Wójcik — 2000

Annales Polonici Mathematici

We show that under some assumptions on the function f the system $ż = z ̅ (f (z) e^{i ϕ t} + e^{i 2 ϕ t})$ 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.

Periodic segments and Nielsen numbers

Klaudiusz Wójcik — 1999

Banach Center Publications

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

Complicated dynamics in nonautonomous ODEs.

Pienia̧żek, Leszek; Wójcik, Klaudiusz — 2003

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Currently displaying 1 – 5 of 5

On Existence of Positive Periodic Solutions.

An attraction result and an index theorem for continuous flows on $ℝ^{n} \times [0, \infty)$

Chaos in some planar nonautonomous polynomial differential equation

Periodic segments and Nielsen numbers

Complicated dynamics in nonautonomous ODEs.

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

On Existence of Positive Periodic Solutions.

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

Chaos in some planar nonautonomous polynomial differential equation

Periodic segments and Nielsen numbers

Complicated dynamics in nonautonomous ODEs.

An attraction result and an index theorem for continuous flows on $ℝ^{n} \times [0, \infty)$