9 citations · 24 across the 22 of their papers we have counts for
6 papers · 1 filter
On the Invariance of Li-Yorke Chaos of Interval Maps
Bau-Sen Du
In their celebrated "Period three implies chaos" paper, Li and Yorke proved that if a continuous interval map f has a period 3 point then there is an uncountable scrambled set S on…
A Simple Proof of Sharkovsky's Theorem
Bau-Sen Du
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
A Simple Proof of Sharkovsky's Theorem Revisited
Bau-Sen Du
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
The lives of period-3 orbits for some quadratic polynomials
Bau-Sen Du
In this note, we consider the following two families of quadratic polynomials and and show that their respective period-3 orbi…
More simple proofs of Sharkovsky's theorem
Bau-Sen Du
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Shar…
On the nature of chaos
Bau-Sen Du
Based on newly discovered properties of the shift map (Theorem 1), we believe that chaos should involve not only nearby points can diverge apart but also faraway points can get clo…