Fractal attractors induced by β-shifts.

• We describe a class of fractal attractors induced by β -shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log β and have an ergodic measure of full entropy. Moreover we determine the Hausdorff dimension of the attractor. We describe a class of fractal attractors induced by β -shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log β and have an ergodic measure of full entropy. This demonstrates that, symbolic dynamics can be used to determine significant properties of a geometric model in chaotic dynamics. Moreover we determine the Hausdorff dimension of the attractor induced by β -shifts. Since the dimension is in (1,2) these attractors are fractals, we have thus found a new class of fractal attractors in the theory of dynamical systems. [ABSTRACT FROM AUTHOR]

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