5 papers
Dynamics of Kahan-Hirota-Kimura maps with rational invariant fibrations
VÃctor Mañosa, Chara Pantazi
We present a simple method to study the dynamics of planar Kahan-Hirota-Kimura (KHK) maps preserving rational fibrations. Using this approach, we show that integrable KHK maps may…
Liouvillian integrability of vector fields in higher dimensions
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider complex rational vector fields in dimension (equivalently, differential forms of degree in variables) which admit a Liouvillian first integral. Extendin…
Liouvillian integrability of three dimensional vector fields
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider a three dimensional complex polynomial, or rational, vector field (equivalently, a two-form in three variables) which admits a Liouvillian first integral. We prove that…
Liouvillian integrability of rational vector fields: The case of algebraic extensions
Colin Christopher, Chara Pantazi, Sebastian Walcher
As shown in a previous paper, whenever a rational vector field on , , is Liouvillian integrable, then it admits a first integral obtained by two successive integr…
Kahan-Hirota-Kimura maps preserving original cubic hamiltonians
VÃctor Mañosa, Chara Pantazi
We study the class of cubic Hamiltonian vector fields whose associated Kahan-Hirota-Kimura (KHK) maps preserve the original Hamiltonian function. Our analysis focuses on these fiel…