Normal forms of polynomial differential systems in $${\mathbb{R}}^3$$ having at least three invariant algebraic surfaces

Autor: Mohammadreza Molaei, Najmeh Khajoei
Rok vydání: 2020
Předmět:
Zdroj: Rendiconti del Circolo Matematico di Palermo Series 2. 70:1023-1035
ISSN: 1973-4409
0009-725X
DOI: 10.1007/s12215-020-00537-y
Popis: In this paper, we find the normal forms of polynomial differential systems in $${\mathbb{R}}^3$$ which have at least three invariant algebraic surfaces. Also, we deduce the normal forms of polynomial differential systems in $${\mathbb{R}}^3$$ having a parabolic cylinder with the equation $${\mathcal{P}} : y^2-z$$ , or having a hyperbolic parabolic with the equation $${\mathcal{H}} : x^2-y^2-z$$ as invariant objects. The conditions to find a lower bound for the number of invariant algebraic curves for the deduced systems are obtained.
Databáze: OpenAIRE
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