The complex quadratic map and its ℳ-set

Benoit B. Mandelbrot
Additional contact information
Benoit B. Mandelbrot: Yale University, Mathematics Department

Chapter C5 in Fractals and Chaos, 2004, pp 73-95 from Springer

Abstract: Abstract For each complex μ, denote by F(μ) the largest bounded set in the complex plane that is invariant under the action of the map z → f(z) = z2-μ. M 1980n{C3} and M 1982F{FGN}, Chapter 19 {C4} reported various remarkable properties of the M0 set (the set of those values of the complex μ for which F(μ) contains domains) and of the closure ℳ of ℳ0. {P.S. 2003: see Chapter foreword.} The goals of this work are as follows.

Keywords: Universality Class; Stable Cycle; Stable Limit Cycle; Stable Fixed Point; Whirlpool Circle (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-4017-2_5

Ordering information: This item can be ordered from
http://www.springer.com/9781475740172

DOI: 10.1007/978-1-4757-4017-2_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().