On the inverse stability of $ z^n+c $

Yang Gao; Qingzhong Ji; Yang Gao; Qingzhong Ji

doi:10.3934/era.2025066

Electronic Research Archive

2025, Volume 33, Issue 3: 1414-1428. doi: 10.3934/era.2025066

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Research article

On the inverse stability of $ z^n+c $

Yang Gao ,
Qingzhong Ji ^,

School of Mathematics, Nanjing University, Nanjing 210093, China

Received: 03 January 2025 Revised: 18 February 2025 Accepted: 21 February 2025 Published: 12 March 2025

Let $ \phi(z) = z^d + c $ be a polynomial over a field $ K. $ We study the inverse stability of $ \phi(z) $ over $ K. $ In this paper, we establish some sufficient conditions for the inverse stability of $ \phi(z) $ over the field of rational numbers and a function field. Furthermore, we also provide necessary and sufficient conditions for the inverse stability of $ \phi(z) $ over a finite field.
- stability,
- polynomial irreducibility,
- iterations,
- arithmetic dynamics
Citation: Yang Gao, Qingzhong Ji. On the inverse stability of $ z^n+c $[J]. Electronic Research Archive, 2025, 33(3): 1414-1428. doi: 10.3934/era.2025066

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Abstract

Let $ \phi(z) = z^d + c $ be a polynomial over a field $ K. $ We study the inverse stability of $ \phi(z) $ over $ K. $ In this paper, we establish some sufficient conditions for the inverse stability of $ \phi(z) $ over the field of rational numbers and a function field. Furthermore, we also provide necessary and sufficient conditions for the inverse stability of $ \phi(z) $ over a finite field.

References

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