Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-01T07:04:18.225Z Has data issue: false hasContentIssue false
  • English
  • Français

On the accumulation sets of exponential rays

Published online by Cambridge University Press:  20 June 2017

JIANXUN FU  and
GAOFEI ZHANG
JIANXUN FU
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, PR China email jianxunf@163.com
GAOFEI ZHANG
Affiliation:
Department of Mathematics, Qufu Normal University, Qufu, 273165, PR China email zhanggf@nju.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that there exist non-landing exponential rays with bounded accumulation sets. By introducing folding models of certain rays, we prove that each of the corresponding accumulation sets is an indecomposable continuum containing part of the ray, an indecomposable continuum disjoint from the ray or a Jordan arc.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 2 , February 2019 , pp. 370 - 391
Copyright
© Cambridge University Press, 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benini, A. M. and Rocha, M. M.. Satellite parabolic perturbations in exponential dynamics. Preprint, 2012.Google Scholar
Bodelón, C., Devaney, R. L., Goldberg, L., Hayes, M., Hubbard, J. and Roberts, G.. Hairs for the complex exponential family. Internat. J. Bifur. Chaos Appl. Sci. Engrg 9 (1999), 1517–1534.Google Scholar
Curry, S.. One-dimensional nonseparating plane continua with disjoint 𝜀-dense subcontinua. Topology Appl. 39 (1991), 145–151.Google Scholar
Devaney, R. L.. Knaster-like continua and complex dynamics. Ergod. Th. & Dynam. Sys. 13 (1993), 627–634.Google Scholar
Devaney, R. L.. Complex exponential dynamics. Handbook of Dynamical Systems. Vol. 3. Eds. Broer, H., Hasselblatt, B. and Takens, F.. Elsevier, North-Holland, 2010, pp. 125–224.Google Scholar
Devaney, R. L. and Jarque, X.. Indecomposable continua in exponential dynamics. Conform. Geom. Dyn. 6 (2002), 1–12 (electronic).Google Scholar
Devaney, R. L., Jarque, X. and Rocha, M. M.. Indecomposable continua and Misiurewicz points in exponential dynamics. Internat. J. Bifur. Chaos Appl. Sci. Engrg 15(10) (2005), 3281–3293.Google Scholar
Devaney, R. L. and Krych, M.. Dynamics of exp(z). Ergod. Th. & Dynam. Sys. 4(1) (1984), 35–52.Google Scholar
Milnor, J.. Dynamics in One Complex Variable, 3rd edn. Princeton University Press, Princeton, NJ, 2006.Google Scholar
Rempe, L.. Dynamics of exponential maps. Doctoral Thesis, Christian-Albrechts-Universität Kiel, 2003.Google Scholar
Rempe, L.. A landing theorem for periodic rays of exponential maps. Proc. Amer. Math. Soc. 134 (2006), 2639–2648.Google Scholar
Rempe, L.. On non-landing dynamic rays of exponential maps. Ann. Acad. Sci. Fenn. 32 (2007), 353–369.Google Scholar
Rempe, L. and Worsley, S.. Preprint, 2015.Google Scholar
Rottenfusser, G., Ruckert, J., Rempe, L. and Schleicher, D.. Dynamic rays of bounded-type entire functions. Ann. of Math. (2) 173 (2010), 77–125.Google Scholar
Schleicher, D. and Zimmer, J.. Escaping points of exponential maps. J. Lond. Math. Soc. (2) 67 (2003), 380–400.Google Scholar
Schleicher, D. and Zimmer, J.. Periodic points and dynamic rays of exponential maps. Ann. Acad. Sci. Fenn. Math. 28 (2003), 327–354.Google Scholar