Fanping Zeng

collaborators

3 papers

math.DS2024

$(ω, α, n)$ -sensitivity and limit sets of zero entropy homeomorphisms on the square

Jiehua Mai, Enhui Shi, Kesong Yan +1

For a homeomorphism $f$ of a compact metric space $X$ and a positive integer $n \geq 2$ , we introduce the notion of $(ω, α, n)$ -sensitivity of $f$ , which describes such a kind of ch…

math.DS2024

A new construction of counterexamples to the bounded orbit conjecture

Jiehua Mai, Enhui Shi, Kesong Yan +1

The bounded orbit conjecture says that every homeomorphism on the plane with each of its orbits being bounded must have a fixed point. Brouwer's translation theorem asserts that th…

math.DS2024

Can points of bounded orbits surround points of unbounded orbits ?

Jiehua Mai, Enhui Shi, Kesong Yan +1

We show a somewhat surprising result: if $E$ is a disk in the plane $R^{2}$ , then there is a homeomorphism $h : R^{2} \to R^{2}$ such that, for every $x\in\pa…

(ω,α,n)-sensitivity and limit sets of zero entropy homeomorphisms on the square

A new construction of counterexamples to the bounded orbit conjecture

Can points of bounded orbits surround points of unbounded orbits ?

$(ω, α, n)$ -sensitivity and limit sets of zero entropy homeomorphisms on the square