The universality of strange attractors is explored. In order to explain the scaling properties of these attractors, renormalization theory is extended between two-dimensional Hamiltonian and one-dimensional strongly dissipative systems. The theory describes the crossover behavior between Hamiltonian and one-dimensional maps. The universal Hamiltonian map T* serves as the generator for dissipative maps via repeated iterations of a renormalization operator. These maps exhibit universal scaling for period doubling, strange attractors and their crisis, Liapunov exponents, and dimensions.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics