Illinois Journal of Mathematics

The Illinois Journal of Mathematics (IJM) was founded in 1957 by Reinhold Baer, Joseph L. Doob, Abraham Taub, George Whitehead, and Oscar Zariski. The journal is sponsored by the Department of Mathematics at the University of Illinois at Urbana-Champaign. It aims to disseminate at reasonable cost significant new, peer-reviewed results in all active areas of mathematics research. In addition to its regular editions it has published special volumes in honor of distinguished members of its host department including R. Baer, D. Burkholder, J. D’Angelo, J. Doob, P. Griffith, W. Haken, and P. Schupp. The journal’s editorial board, which counts distinguished mathematicians such as J. Bourgain, A. Calderon, S.S. Chern, H. Kesten, and K. Uhlenbeck among its past members, comprises a mix of preeminent mathematicians from within its host department and across the mathematical research establishment.

Beginning in 2019 IJM is published by Duke University Press on behalf of the Department of Mathematics at the University of Illinois at Urbana-Champaign.

  • ISSN: 0019-2082 (print), 1945-6581 (electronic)
  • Publisher: Duke University Press
  • Discipline(s): Mathematics
  • Full text available in Euclid: 1957--
  • Access: Articles older than 5 years are open
  • Euclid URL: https://projecteuclid.org/ijm

Featured bibliometrics

MR Citation Database MCQ (2018): 0.53
SJR/SCImago Journal Rank (2017): 0.531

Indexed/Abstracted in: Current Contents: ArticleFirst, Current Index to Statistics, INIS Collection Search, MathSciNet, Referativnyi Zhurnal, Russian Academy of Sciences Bibliographies, Scopus, and zbMATH

Featured article

Examples of non-autonomous basins of attraction

Sayani Bera , Ratna Pal , and Kaushal Verma Volume 61, Number 3-4 (2017)
Abstract

The purpose of this paper is to present several examples of non-autonomous basins of attraction that arise from sequences of automorphisms of $\mathbb{C}^{k}$. In the first part, we prove that the non-autonomous basin of attraction arising from a pair of automorphisms of $\mathbb{C}^{2}$ of a prescribed form is biholomorphic to $\mathbb{C}^{2}$. This, in particular, provides a partial answer to a question raised in (A survey on non-autonomous basins in several complex variables (2013) Preprint) in connection with Bedford’s Conjecture about uniformizing stable manifolds. In the second part, we describe three examples of Short $\mathbb{C}^{k}$’s with specified properties. First, we show that for $k\geq3$, there exist $(k-1)$ mutually disjoint Short $\mathbb{C}^{k}$’s in $\mathbb{C}^{k}$. Second, we construct a Short $\mathbb{C}^{k}$, large enough to accommodate a Fatou–Bieberbach domain, that avoids a given algebraic variety of codimension $2$. Lastly, we discuss examples of Short $\mathbb{C}^{k}$’s with (piece-wise) smooth boundaries.

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