On the Properties of Konishi-kaneko Map

An interesting possibility of study of the dynamics of N-body gravitating systems is provided by the Konishi-Kaneko iterated map [1-5]. Particular interest has the demonstrated by Inagaki [4] agreement of Konishi-Kaneko map with the thermodynamic considerations and the results of numerical simulations. At least two points outline the importance of iterated maps: 1. Iterated maps can enable one to avoid in certain way the principal difficulties associated with N-body systems – the non-compactness of the phase space and singularity of Newtonian interaction. 2. Iterated maps can be rather informative in revealing the mechanisms of developing of chaos. The Konishi-Kaneko map is defined as follows [1,2]: p n+1 i