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Fractal and riddled basins: arithmetic signatures in the parameter space of two coupled quadratic maps. (English) Zbl 0978.37031

Summary: We investigate the parameter space of two coupled quadratic (logistic) maps. Of special interest is the analytical characterization of the precursors leading to riddled basins. We delimit stability domains for orbits with the two lowest periods. In addition, we study the singularities of the phase-space surfaces obtained by eliminating all parameters from the equations of motion.

MSC:

37E15 Combinatorial dynamics (types of periodic orbits)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37C75 Stability theory for smooth dynamical systems
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