dc.contributor.author |
Fagella Rabionet, Núria |
dc.contributor.author |
Martí-Pete, David |
dc.date |
2017 |
dc.identifier |
https://ddd.uab.cat/record/221362 |
dc.identifier |
urn:10.3934/dcds.2017134 |
dc.identifier |
urn:oai:ddd.uab.cat:221362 |
dc.identifier |
urn:scopus_id:85017546787 |
dc.identifier |
urn:articleid:15535231v37n6p3123 |
dc.identifier |
urn:gsduab:4601 |
dc.identifier |
urn:wos_id:000395905000010 |
dc.identifier |
urn:altmetric_id:6160410 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Ministerio de Economía y Competitividad MTM2011-26995-C02-02 |
dc.relation |
Ministerio de Economía y Competitividad MTM2014-52209-C2-2-P |
dc.relation |
Discrete and continuous dynamical systems. Series A ; Vol. 37, Issue 6 (June 2017), p. 3123-3160 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
Complex dynamics |
dc.subject |
Transcendental functions |
dc.subject |
Punctured plane |
dc.subject |
Escaping set |
dc.subject |
Dynamic rays |
dc.subject |
Bounded-type functions |
dc.title |
Dynamic rays of bounded-type transcendental self-maps of the punctured plane |
dc.type |
Article |
dc.description.abstract |
We study the escaping set of functions in the class B∗, that is, transcendental self-maps of ℂ∗ for which the set of singular values is contained in a compact annulus of ℂ∗ that separates zero from infinity. For functions in the class B∗, escaping points lie in their Julia set. If f is a composition of finite order transcendental self-maps of ℂ∗ (and hence, in the class B∗), then we show that every escaping point of f can be connected to one of the essential singularities by a curve of points that escape uniformly. Moreover, for every sequence e ∈ {0,∞}, we show that the escaping set of f contains a Cantor bouquet of curves that accumulate to the set {0,∞} according to e under iteration by f. |