Abstract
We study numerically the three types of asymmetry associated with the map x’ = 1 – εi - ai |x|zi (i=1, 2 respectively correspond to x>0 and x≦0). The first case is the amplitude asymmetry (a1≠a2), the second case is the exponent asymmetry (z1≠z2) and the last one is a discontinuous map (ε1≠ε2). In the two first cases the period-doubling road to chaos is topologically unmodified. In the last case the road to chaos is completely new (“gap road”). Chaos now is attained through sequences of inverse cascades. Various new features are observed, concerning the phase diagram, kneading sequences, Liapunov and uncertainty exponents, number of attractors, multifractality, among others. We also study the crossover between the discontinuous map and the continuous one.
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© 1989 Kluwer Academic Publishers
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de Sousa Vieira, M.C., Tsallis, C. (1989). The Gap Road to Chaos and Its Main Characteristics. In: Tirapegui, E., Villarroel, D. (eds) Instabilities and Nonequilibrium Structures II. Mathematics and Its Applications, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2305-8_6
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DOI: https://doi.org/10.1007/978-94-009-2305-8_6
Publisher Name: Springer, Dordrecht
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