Chaotic transients in multidimensional maps

The paper contains results of numerical experiments on chaotic transients in two nonlinear maps Fi : R3 → R3. The characteristic rambling time NΓ of the transients in the map exhibiting hyperchaotic behaviour were found to be over two orders of magnitude longer than their counterparts in the map exhibiting ordinary chaotic behaviour. An attempt is made to identify the mechanism responsible for such a discrepancy in this respect between both maps. It is argued that the difference of the topological dimension of the chaotic and hyperchaotic attractor may be the primary cause of this phenomenon