Calculation of algebraic entropies of d-PIVand d-PV

Chengliang Tan; Jilong Zhang

doi:10.1063/5.0040204

Calculation of algebraic entropies of d-P_IVand d-P_V

Chengliang Tan
, Jilong Zhang^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

1 Scopus citations

Abstract

In this paper, we describe the singularity patterns of d-PIV in detail and calculate the algebraic entropies of d-PIV and d-PV, which are shown to be both zeros. However, for the discrete equations that are similar with d-PIV, not all algebraic entropies are zeros. An example shows that even if the equation passes the singularity confinement test, it still has a positive algebraic entropy. We also explore the influence of cyclic patterns and anti-confined patterns in the calculation.

Original language	English
Article number	063501
Journal	Journal of Mathematical Physics
Volume	62
Issue number	6
DOIs	https://doi.org/10.1063/5.0040204
State	Published - 1 Jun 2021

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10.1063/5.0040204

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abstract = "In this paper, we describe the singularity patterns of d-PIV in detail and calculate the algebraic entropies of d-PIV and d-PV, which are shown to be both zeros. However, for the discrete equations that are similar with d-PIV, not all algebraic entropies are zeros. An example shows that even if the equation passes the singularity confinement test, it still has a positive algebraic entropy. We also explore the influence of cyclic patterns and anti-confined patterns in the calculation.",

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AB - In this paper, we describe the singularity patterns of d-PIV in detail and calculate the algebraic entropies of d-PIV and d-PV, which are shown to be both zeros. However, for the discrete equations that are similar with d-PIV, not all algebraic entropies are zeros. An example shows that even if the equation passes the singularity confinement test, it still has a positive algebraic entropy. We also explore the influence of cyclic patterns and anti-confined patterns in the calculation.

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Calculation of algebraic entropies of d-PIVand d-PV

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Calculation of algebraic entropies of d-P_IVand d-P_V