{"page":"2827 - 2849","year":"2018","type":"journal_article","day":"01","quality_controlled":"1","oa_version":"Submitted Version","date_updated":"2023-09-12T07:45:37Z","scopus_import":"1","publisher":"AIMS","_id":"303","date_published":"2018-06-01T00:00:00Z","date_created":"2018-12-11T11:45:43Z","publist_id":"7576","article_processing_charge":"No","doi":"10.3934/dcds.2018120","month":"06","intvolume":"        38","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1706.03062"}],"issue":"6","publication_status":"published","publication":"Discrete and Continuous Dynamical Systems- Series A","status":"public","acknowledgement":"The first author, Nikita Kalinin, is funded by SNCF PostDoc.Mobility grant 168647. Support from the Basic Research Program of the National Research University Higher School of Economics is gratefully acknowledged. The second author, Mikhail Shkolnikov, is supported in part by the grant 159240 of the Swiss National Science Foundation as well as by the National Center of Competence in Research SwissMAP of the Swiss National Science Foundation.","volume":38,"external_id":{"isi":["000438818400007"],"arxiv":["1706.03062"]},"isi":1,"abstract":[{"lang":"eng","text":"The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results we need for other articles and also introduces several objects interesting by themselves."}],"citation":{"ieee":"N. Kalinin and M. Shkolnikov, “Introduction to tropical series and wave dynamic on them,” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 38, no. 6. AIMS, pp. 2827–2849, 2018.","ista":"Kalinin N, Shkolnikov M. 2018. Introduction to tropical series and wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A. 38(6), 2827–2849.","chicago":"Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” <i>Discrete and Continuous Dynamical Systems- Series A</i>. AIMS, 2018. <a href=\"https://doi.org/10.3934/dcds.2018120\">https://doi.org/10.3934/dcds.2018120</a>.","mla":"Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 38, no. 6, AIMS, 2018, pp. 2827–49, doi:<a href=\"https://doi.org/10.3934/dcds.2018120\">10.3934/dcds.2018120</a>.","short":"N. Kalinin, M. Shkolnikov, Discrete and Continuous Dynamical Systems- Series A 38 (2018) 2827–2849.","ama":"Kalinin N, Shkolnikov M. Introduction to tropical series and wave dynamic on them. <i>Discrete and Continuous Dynamical Systems- Series A</i>. 2018;38(6):2827-2849. doi:<a href=\"https://doi.org/10.3934/dcds.2018120\">10.3934/dcds.2018120</a>","apa":"Kalinin, N., &#38; Shkolnikov, M. (2018). Introduction to tropical series and wave dynamic on them. <i>Discrete and Continuous Dynamical Systems- Series A</i>. AIMS. <a href=\"https://doi.org/10.3934/dcds.2018120\">https://doi.org/10.3934/dcds.2018120</a>"},"author":[{"full_name":"Kalinin, Nikita","last_name":"Kalinin","first_name":"Nikita"},{"orcid":"0000-0002-4310-178X","last_name":"Shkolnikov","full_name":"Shkolnikov, Mikhail","id":"35084A62-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","language":[{"iso":"eng"}],"department":[{"_id":"TaHa"}],"title":"Introduction to tropical series and wave dynamic on them"}