REVERSE ITERATED FUNCTION SYSTEM AND DIMENSION OF DISCRETE FRACTALS

Publisher： Cambridge University Press

E-ISSN： 1755-1633|79|1|37-47

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.79, Iss.1, 2009-02, pp. : 37-47

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

A reverse iterated function system is defined as a family of expansive maps {T1,T2,…,Tm} on a uniformly discrete set $M\subset \Bbb {R}^d$. An invariant set is defined to be a nonempty set $F\subseteq M$ satisfying F= j=1mTj(F). A computation method for the dimension of the invariant set is given and some questions asked by Strichartz are answered.

Related content

Iterated Function System and Ruelle Operator

By Fan A.H.   Ball K-S.J.A.  

Journal of Mathematical Analysis and Applications, Vol. 231, Iss. 2, 1999-03 ,pp. : 319-344 (26)

Academic Press

Access to resources Recommend Favorite

ON A CERTAIN GENERALISATION OF THE ITERATED FUNCTION SYSTEM

By  

Bulletin of the Australian Mathematical Society, Vol. 87, Iss. 1, 2012-08 ,pp. : 37-54 (18)

Cambridge University Press

Access to resources Recommend Favorite

THE CONLEY ATTRACTORS OF AN ITERATED FUNCTION SYSTEM

By  

Bulletin of the Australian Mathematical Society, Vol. 88, Iss. 2, 2013-10 ,pp. : 267-279 (13)

Cambridge University Press

Access to resources Recommend Favorite

Hausdorff dimension of random fractals with overlaps

By  

Bulletin of the Australian Mathematical Society, Vol. 65, Iss. 2, 2002-04 ,pp. : 315-328 (14)

Cambridge University Press

Access to resources Recommend Favorite

Elliptic Norms and the Convergence of Iterated Function Systems in the Plane

By Baldo S.   Horváth C.J.  

Journal of Mathematical Analysis and Applications, Vol. 236, Iss. 2, 1999-08 ,pp. : 557-584 (28)

Academic Press

Access to resources Recommend Favorite