Calculation of algebraic entropies of d-PIV and d-PV

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...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-06, Vol.62 (6)
Main Authors: Tan, Chengliang, Zhang, Jilong
Format: Article
Language:English
Subjects:
Algebra
Mathematical analysis
Physics
Singularity (mathematics)
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0040204