Joel Mitchell

collaborators

6 papers

math.DS2020

When is the beginning the end? On full trajectories, limit sets and internal chain transitivity

Joel Mitchell

Let $f : X \to X$ be a continuous map on a compact metric space $X$ and let $α_{f}$ , $ω_{f}$ and $I C T_{f}$ denote the set of $α$ -limit sets, $ω$ -limit sets and nonempty closed inter…

math.DS2020

Expansivity and unique shadowing

Chris Good, Sergio Macías, Jonathan Meddaugh +2

Let $f : X \to X$ be a continuous function on a compact metric space. We show that shadowing is equivalent to backwards shadowing and two-sided shadowing when the map $f$ is ont…

math.DS2019

Orbital shadowing, $ω$ -limit sets and minimality

Joel Mitchell

Let $X$ be a compact Hausdorff space, with uniformity $U$ , and let $f : X \to X$ be a continuous function. For $D \in U$ , a $D$ -pseudo-orbit is a sequence…

math.DS2019

Shadowing, internal chain transitivity and $α$ -limit sets

Chris Good, Jonathan Meddaugh, Joel Mitchell

Let $f : X \to X$ be a continuous map on a compact metric space $X$ and let $α_{f}$ , $ω_{f}$ and $I C T_{f}$ denote the set of $α$ -limit sets, $ω$ -limit sets and nonempty closed inter…

math.DS2019

Preservation of shadowing in discrete dynamical systems

Chris Good, Joel Mitchell, Joe Thomas

We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products an…

math.DS2019

On inverse shadowing

Chris Good, Joel Mitchell, Joe Thomas

We give a reformulation of the inverse shadowing property with respect to the class of all pseudo-orbits. This reformulation bears witness to the fact that the property is far stro…

When is the beginning the end? On full trajectories, limit sets and internal chain transitivity

Expansivity and unique shadowing

Orbital shadowing, ω-limit sets and minimality

Shadowing, internal chain transitivity and α-limit sets

Preservation of shadowing in discrete dynamical systems

On inverse shadowing

Orbital shadowing, $ω$ -limit sets and minimality

Shadowing, internal chain transitivity and $α$ -limit sets