A. V. Arutyunov, S. E. Zhukovskiy, D. Yu. Karamzin, “Some properties of two-dimensional surjective <nobr>$p$</nobr>-homogeneous maps”, Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 7,Pages <nobr>1083

Some properties of two-dimensional surjective $p$-homogeneous maps

A. V. Arutyunov^ab, S. E. Zhukovskiy^b, D. Yu. Karamzin^bc

^a Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia
^b RUDN University, Moscow, Russia
^c Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia

Abstract: The properties of real $p$-homogeneous polynomial maps in $\mathrm{R}^2$ are examined. The relation between surjectivity and the existence of a nontrivial zero is investigated. Additionally, the relation between surjectivity and stable surjectivity is studied. Examples are discussed.

Key words: $p$-homogeneous maps, surjectivity and nontrivial zeros of homogeneous maps.

UDC: 519.642.8

Received: 02.02.2017

DOI: 10.7868/S0044466917070043