{"department":[{"_id":"LaEr"}],"ec_funded":1,"abstract":[{"text":"We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the th Lyapunov exponent is finite and the st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part.","lang":"eng"}],"oa":1,"oa_version":"Preprint","date_published":"2019-04-01T00:00:00Z","type":"journal_article","publisher":"Cambridge University Press","issue":"4","page":"1082-1098","day":"01","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"intvolume":"        39","language":[{"iso":"eng"}],"date_created":"2019-03-10T22:59:18Z","title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","article_processing_charge":"No","status":"public","isi":1,"publication_status":"published","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1601.06118"}],"volume":39,"citation":{"ieee":"C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite Lyapunov exponents,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 39, no. 4. Cambridge University Press, pp. 1082–1098, 2019.","short":"C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098.","apa":"Sadel, C., &#38; Xu, D. (2019). Singular analytic linear cocycles with negative infinite Lyapunov exponents. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/etds.2017.52\">https://doi.org/10.1017/etds.2017.52</a>","chicago":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2019. <a href=\"https://doi.org/10.1017/etds.2017.52\">https://doi.org/10.1017/etds.2017.52</a>.","ama":"Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov exponents. <i>Ergodic Theory and Dynamical Systems</i>. 2019;39(4):1082-1098. doi:<a href=\"https://doi.org/10.1017/etds.2017.52\">10.1017/etds.2017.52</a>","mla":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:<a href=\"https://doi.org/10.1017/etds.2017.52\">10.1017/etds.2017.52</a>.","ista":"Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098."},"publication":"Ergodic Theory and Dynamical Systems","month":"04","_id":"6086","year":"2019","doi":"10.1017/etds.2017.52","quality_controlled":"1","author":[{"first_name":"Christian","orcid":"0000-0001-8255-3968","last_name":"Sadel","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","full_name":"Sadel, Christian"},{"last_name":"Xu","first_name":"Disheng","full_name":"Xu, Disheng"}],"external_id":{"arxiv":["1601.06118"],"isi":["000459725600012"]},"date_updated":"2023-08-25T08:03:30Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"}