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Holes

In: Chaos in Discrete Dynamical Systems

Author

Listed:
  • Ralph H. Abraham

    (University of California Santa Cruz)

  • Laura Gardini

    (Universitá di Urbino, Instituto di Scienze Economiche)

  • Christian Mira

    (Institut National des Sciences Appliquees de Toulouse, Dept. of Control Engineering)

Abstract

We have already encountered holes in the Case 1 of the first map family treated at the end of the preceding chapter (see Figure 4–17). We now change the parameter a from 0.7 to 1.0, obtaining Case 2 of the first map family, in which the bifurcations involving holes are somewhat clearer. This change eliminates the repelling 2-cycle, {Q1, Q2}. As before, the fixed point Q becomes a repelling focus, but the fixed point P is now a saddle.1

Suggested Citation

  • Ralph H. Abraham & Laura Gardini & Christian Mira, 1997. "Holes," Springer Books, in: Chaos in Discrete Dynamical Systems, chapter 0, pages 59-83, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1936-1_5
    DOI: 10.1007/978-1-4612-1936-1_5
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