Geodesic
On the asymptotic of homological solutions to linear multidimensional difference equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 4, pp. 417-430

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Given a linear homogeneous multidimensional difference equation with constant coefficients, we choose a pair $(\gamma,\omega)$, where $\gamma$ is a homological $k$-dimensional cycle on the characteristic set of the equation and $\omega$ is a holomorphic form of degree $k$. This pair defines a so called homological solution by the integral over $\gamma$ of the form $\omega$ multiplied by an exponential kernel. A multidimensional variant of Perron's theorem in the class of homological solutions is illustrated by an example of the first order equation.
Keywords: difference equation, asymptotic, amoebas of algebraic sets
Mots-clés : logarithmic Gauss map. 
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Natalia A. Bushueva; Konstantin V. Kuzvesov; Avgust K. Tsikh. On the asymptotic of homological solutions to linear multidimensional difference equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 4, pp. 417-430. http://geodesic.mathdoc.fr/item/JSFU_2014_7_4_a1/