The resonance spectrum of the cusp map in the space of analytic functions
نویسندگان
چکیده
We prove that the Frobenius–Perron operator of the cusp map F : [−1, 1] → [−1, 1], F (x) = 1 − 2 √ |x| (which is an approximation of the Poincaré section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that the spectrum of the Frobenius–Perron operator in the space of real-analytic functions on [0, 1] as well as in the space of entire functions is the whole complex plane.
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