Jiehua Mai

collaborators

7 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…

math.DS2024

Orientation Preserving Homeomorphisms of the Plane having BP-Chain Recurrent Points

Jiehua Mai, Kesong Yan, Fanping Zeng

More than a century ago, L. E. J. Brouwer proved a famous theorem, which says that any orientation preserving homeomorphism of the plane having a periodic point must have a fixed p…

math.DS2024

Some extensions of the Brouwer fixed point theorem

Jiehua Mai, Enhui Shi, Kesong Yan +1

We study the existence of fixed points for continuous maps $f$ from an $n$ -ball $X$ in $R^{n}$ to $R^{n}$ with $n \geq 1$ . We show that $f$ has a fixed point if, for som…

math.DS2024

Quasi-intermediate value theorem and outflanking arc theorem for plane maps

Jiehua Mai, Enhui Shi, Kesong Yan +1

For a disk $D$ in the plane $R^{2}$ and a plane map $f$ , we give several conditions on the restriction of $f$ to the boundary $\partial D$ of $D$ which imply the existence of…

(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 ?

Orientation Preserving Homeomorphisms of the Plane having BP-Chain Recurrent Points

Some extensions of the Brouwer fixed point theorem

Quasi-intermediate value theorem and outflanking arc theorem for plane maps

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