Accumulation Sets

Luís Barreira
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Luís Barreira: Universidade de Lisboa, Instituto Superior Técnico

Chapter Chapter 13 in Lyapunov Exponents, 2017, pp 253-264 from Springer

Abstract: 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.

Date: 2017
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DOI: 10.1007/978-3-319-71261-1_13

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