NUMERICAL ESTIMATES OF THE GENERALIZED DIMENSIONS OF THE HENON ATTRACTOR FOR NEGATIVE-Q

The usual fixed-size box-counting algorithms are inefficient for compu ting generalized fractal dimensions in the range of q < 0. In this let ter we describe a new numerical algorithm specifically devised to esti mate generalized dimensions for large negative q, providing evidence o f its better performance. We compute the complete spectrum of the Heno n attractor, and interpret our results in terms of a 'phase transition ' between different multiplicative laws.