Skip to content
DraconiticResearch
Search Sources API
206,690 studies31 sourcesUpdated 22 min ago
PreprintarXiv licencearXiv

On the Julia sets of the non-autonomous iteration of exponential maps

  • Jiaxing Huang
  • Xiao Yao
Open at sourcePDFDOICite

Abstract

This paper studies non-autonomous iterations of λez, where at each step the parameter λ is chosen from a bounded interval. Urbański and Zdunik introduced and developed a thermodynamic formalism for random dynamics of exponential maps, extending the autonomous result established independently by Rees and Lyubich to typical parameter sequences in [A, B]ℕ with 1/e<A<B<∞. In this paper, we show that the same conclusion indeed holds for all parameters in [A, B]ℕ, Our proof is based on carefully crafted uniform versions of pullback arguments, inspired by the original methods of Rees and Lyubich. In a related direction, Urbański and Zdunik established a non-autonomous analogue of Misiurewicz's theorem for the exponential map, later refined by Lech. We further extend their work by providing a refined condition for the Julia set to be the entire complex plane.

Related

  1. Uniformization of Julia sets of geometrically finite rational maps
    Yusheng Luo, Dimitrios Ntalampekos
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  2. The Intersection of nested filled-in little Julia sets have zero area
    Carsten Lunde Petersen
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  3. Wandering exposed Julia components of rational maps
    Jinsong Zeng
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv
  4. Continuity of the Julia sets in non-archimedean and hybrid settings
    Alexandre Roy
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryDynamical systemsarXiv
  5. Sierpiński carpet Julia sets of transcendental entire functions
    Weiwei Su, Fei Yang
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{huang2026julia,
  title = {{On the Julia sets of the non-autonomous iteration of exponential maps}},
  author = {Jiaxing Huang and Xiao Yao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14794},
  eprint = {2610.14794},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14794},
}
RIS
TY  - UNPB
TI  - On the Julia sets of the non-autonomous iteration of exponential maps
AU  - Jiaxing Huang
AU  - Xiao Yao
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14794
UR  - https://arxiv.org/abs/2610.14794
AB  - This paper studies non-autonomous iterations of λe^z, where at each step the parameter λ is chosen from a bounded interval. Urbański and Zdunik introduced and developed a thermodynamic formalism for random dynamics of exponential maps, extending the autonomous result established independently by Rees and Lyubich to typical parameter sequences in [A, B]^ℕ with 1/e<A<B<∞. In this paper, we show that the same conclusion indeed holds for all parameters in [A, B]^ℕ, Our proof is based on carefully crafted uniform versions of pullback arguments, inspired by the original methods of Rees and Lyubich. In a related direction, Urbański and Zdunik established a non-autonomous analogue of Misiurewicz's theorem for the exponential map, later refined by Lech. We further extend their work by providing a refined condition for the Julia set to be the entire complex plane.
ER  -