Glasnik Matematicki, Vol. 53, No. 2 (2018), 343-357.

ON UNBOUNDED POLYNOMIAL DYNAMICAL SYSTEMS

Hamza Boujemaa and Said El Qotbi

Département de Mathématiques, Mohammed V University in Rabat, 1014RP Rabat, Morocco
e-mail: boujemaa@fsr.ac.ma

Systèmes Dynamiques, A3D, Mohammed V University in Rabat, 1014RP Rabat, Morocco
e-mail: Qotbis@gmail.com

Abstract.   Suppose given a polynomial dynamical system of degree m. It is known that if the algebra associated to the corresponding homogeneous dynamical system of degree m has an idempotent element then the original dynamical system is unbounded. In this work, we give a sufficient condition ensuring the unboundedness even when there is no idempotent. Some applications are also given.

2010 Mathematics Subject Classification.   34A34, 17A99

Key words and phrases.   Polynomial dynamical systems, homogenization, unboundedness

DOI: 10.3336/gm.53.2.07

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