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I need to show that tent map has chaotic orbit.I can form a orbit which has lyapunov exponent>0 but don't know how to assure that an orbit is not asymptotically periodic which is the other part of the definition of chaotic orbit.I am guessing an orbit with irrational seed will do the job but not sure how to prove the latter part.Any help?

099 Kazi Hafizur Rahman
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    A common approach to this problem is to express the real numbers in $[0,1]$ in terms of their binary expansion and then investigate the effect of the tent map on those binary expansions. There are some detail in section 2.8, 2.9, and 2.10 of this chapter. – Mark McClure Feb 05 '23 at 15:58

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