---
_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
arxiv: 1
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. <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>
  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>.
  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.
  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.
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'
...