skip to main content

Search for: All records

Creators/Authors contains: "Benedicks, Michael"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Abstract

    We study the classical Hénon family$$f_{a,b}:(x,y)\mapsto (1-ax^2+y,bx)$$fa,b:(x,y)(1-ax2+y,bx),$$00<a<2,$$00<b<1, and prove that given an integer$$k\ge 1$$k1, there is a set of parameters$$E_k$$Ekof positive two-dimensional Lebesgue measure so that$$f_{a,b}$$fa,b, for$$(a,b)\in E_k$$(a,b)Ek, has at leastkattractive periodic orbits and one strange attractor of the type studied in Benedicks and Carleson (Ann Math (2) 133(1):73–169, 1991). A corresponding statement also holds for the Hénon-like families of Mora and Viana (Acta Math 171:1–71, 1993), and we use the techniques of Mora and Viana (1993) to study homoclinic unfoldings also in the case of the original Hénon maps. The final main result of the paper is the existence, within the classical Hénon family, of a positive Lebesgue measure set of parameters whose corresponding maps have two coexisting strange attractors.

    more » « less