10/23/2022, 07:09 PM
Should those points converge on the boundary of the respective petals?
I don't think we can say they are part of the same orbit.
Assume the initial path is the unitary circle. Those intersection points are of the general form
\[\{ p\in \mathbb S^1\, |\, \exists n\in \mathbb N. \exists \theta\in [0,2\pi).\, f^n(e^{i\theta})=p\}\]
Maybe to each \(\theta\) we could associate/study the set of \(n\) such that \(|f^n(e^{i\theta})|=1\).
Not sure how this can be useful.
I don't think we can say they are part of the same orbit.
Assume the initial path is the unitary circle. Those intersection points are of the general form
\[\{ p\in \mathbb S^1\, |\, \exists n\in \mathbb N. \exists \theta\in [0,2\pi).\, f^n(e^{i\theta})=p\}\]
Maybe to each \(\theta\) we could associate/study the set of \(n\) such that \(|f^n(e^{i\theta})|=1\).
Not sure how this can be useful.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)