Introduction to tropical series and wave dynamic on them

Nikita Kalinin; Mikhail Shkolnikov

doi:10.3934/dcds.2018120

Introduction to tropical series and wave dynamic on them

Nikita Kalinin^*, Mikhail Shkolnikov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2827-2849
Number of pages	23
Journal	Discrete and Continuous Dynamical Systems
Volume	38
Issue number	6
DOIs	https://doi.org/10.3934/dcds.2018120
State	Published - Jun 2018
Externally published	Yes

Keywords

Convex set
Non-Archimedean dynamic
Tropical dynamics
Tropical geometry
Tropical series
Wave operator

Access to Document

10.3934/dcds.2018120

Cite this

@article{64d29219ba744d758d9f89d867b71c43,

title = "Introduction to tropical series and wave dynamic on them",

abstract = "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.",

keywords = "Convex set, Non-Archimedean dynamic, Tropical dynamics, Tropical geometry, Tropical series, Wave operator",

author = "Nikita Kalinin and Mikhail Shkolnikov",

year = "2018",

month = jun,

doi = "10.3934/dcds.2018120",

language = "英语",

volume = "38",

pages = "2827--2849",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

number = "6",

}

TY - JOUR

T1 - Introduction to tropical series and wave dynamic on them

AU - Kalinin, Nikita

AU - Shkolnikov, Mikhail

PY - 2018/6

Y1 - 2018/6

N2 - 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.

AB - 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.

KW - Convex set

KW - Non-Archimedean dynamic

KW - Tropical dynamics

KW - Tropical geometry

KW - Tropical series

KW - Wave operator

UR - http://www.scopus.com/inward/record.url?scp=85046395508&partnerID=8YFLogxK

U2 - 10.3934/dcds.2018120

DO - 10.3934/dcds.2018120

M3 - 文章

AN - SCOPUS:85046395508

SN - 1078-0947

VL - 38

SP - 2827

EP - 2849

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 6

ER -

Introduction to tropical series and wave dynamic on them

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this