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Accumulation Sets

In: Lyapunov Exponents

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Listed:
  • Luís Barreira

    (Universidade de Lisboa, Instituto Superior Técnico)

Abstract

For conformal repellers on which the dynamics is topologically mixing, we show that the set of points for which the Lyapunov exponent is not a limit is either empty or residual. This follows from a corresponding result at the level of symbolic dynamics, which shows that for a continuous function on a topologically mixing topological Markov chain, the set of points whose accumulation set of the Birkhoff averages of the function is equal to a given closed interval is residual when the interval is not a singleton. The proof of this result takes advantage of the possibility of concatenating cylinder sets. This chapter can be seen as a complement to the previous chapter, which considers instead the level sets of the Lyapunov exponent at which it is a given limit.

Suggested Citation

  • Luís Barreira, 2017. "Accumulation Sets," Springer Books, in: Lyapunov Exponents, chapter 0, pages 253-264, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-71261-1_13
    DOI: 10.1007/978-3-319-71261-1_13
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