--- _id: '303' 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. 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. article_processing_charge: No author: - first_name: Nikita full_name: Kalinin, Nikita last_name: Kalinin - first_name: Mikhail full_name: Shkolnikov, Mikhail id: 35084A62-F248-11E8-B48F-1D18A9856A87 last_name: Shkolnikov orcid: 0000-0002-4310-178X citation: ama: Kalinin N, Shkolnikov M. Introduction to tropical series and wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A. 2018;38(6):2827-2849. doi:10.3934/dcds.2018120 apa: Kalinin, N., & Shkolnikov, M. (2018). Introduction to tropical series and wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A. AIMS. https://doi.org/10.3934/dcds.2018120 chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series A. AIMS, 2018. https://doi.org/10.3934/dcds.2018120. ieee: N. Kalinin and M. Shkolnikov, “Introduction to tropical series and wave dynamic on them,” Discrete and Continuous Dynamical Systems- Series A, 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. mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series A, vol. 38, no. 6, AIMS, 2018, pp. 2827–49, doi:10.3934/dcds.2018120. short: N. Kalinin, M. Shkolnikov, Discrete and Continuous Dynamical Systems- Series A 38 (2018) 2827–2849. date_created: 2018-12-11T11:45:43Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-12T07:45:37Z day: '01' department: - _id: TaHa doi: 10.3934/dcds.2018120 external_id: arxiv: - '1706.03062' isi: - '000438818400007' intvolume: ' 38' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1706.03062 month: '06' oa: 1 oa_version: Submitted Version page: 2827 - 2849 publication: Discrete and Continuous Dynamical Systems- Series A publication_status: published publisher: AIMS publist_id: '7576' quality_controlled: '1' scopus_import: '1' status: public title: Introduction to tropical series and wave dynamic on them type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 38 year: '2018' ...