Nonlocal operators are chaotic

[EN] We characterize for the first time the chaotic behavior of nonlocal operators that come from a broad class of time-stepping schemes of approximation for fractional differential operators. For that purpose, we use criteria for chaos of Toeplitz operators in Lebesgue spaces of sequences. Surprisingly, this characterization is proved to be-in some cases-dependent of the fractional order of the operator and the step size of the scheme.C. Lizama is partially supported by FONDECYT (Grant No. 1180041) and DICYT, Universidad de Santiago de Chile, USACH. M. Murillo-Arcila is supported by MICINN and FEDER, Projects MTM2016-75963-P and PID2019-105011GB-I00, and by Generalitat Valenciana, Project GVA/2018/110. A. Peris is supported by MICINN and FEDER, Projects MTM2016-75963-P and PID2019-105011GB-I00, and by Generalitat Valenciana, Project PROMETEO/2017/102.Lizama, C.; Murillo Arcila, M.; Peris Manguillot, A. (2020). Nonlocal operators are chaotic. 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