Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas

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

Chapter C12 in Fractals and Chaos, 2004, pp 137-145 from Springer

Abstract: Abstract THE PATH OF SCIENTIFIC INVESTIGATION AND DISCOVERY is not necessarily logical, as history never tires of reminding both laymen and scientists. From many viewpoints, the complex quadratic map, reducible to either z→z2 + c, z → λ(z2-2), or z → λz(1-z), is the simplest of all nonlinear maps. Its global action was therefore the first to be studied carefully, in Fatou 1906. Later, the 1960s and 1970s brought many studies of the restriction of z2-μ to the real quadratic map x 2-μ, and everyone became well aware that the dependence of this real map’s orbits on the parameter μ involves exquisite complications. It has its Myrberg sequence of bifurcations, its May tree, and its Feigenbaum number. Shortly thereafter, my papers reproduced in Part I made the complex quadratic map widely popular.

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_12

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

DOI: 10.1007/978-1-4757-4017-2_12

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 ().