Bulletin of the Australian Mathematical Society

Research Article

On Sharkovsky's cycle coexistence ordering

Peter E. Kloedena1

a1 School of Mathematical and Physical Sciences, Murdoch University, Murdoch, Western Australia.


A theorem of Sharkovsky on the coexistence of cycles for one-dimensional difference equations is generalized to a class of difference equations of arbitary dimension. The mappings defining these difference equations are such that the ith component depends only on the first i independent variables.

(Received January 15 1979)