263 citations · 921 across the 24 of their papers we have counts for
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math-ph2006★ 40 cited
Algebraic Entropy for lattice equations
Claude Viallet
We give the basic definition of algebraic entropy for lattice equations. The entropy is a canonical measure of the complexity of the dynamics they define. Its vanishing is a signal…
math-ph2005★ 34 cited
On the complexity of some birational transformations
Jean Christian Angles D'Auriac, Jean-Marie Maillard, Claude Viallet
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The fir…
math-ph2004★ 22 cited
Solvable Chaos
B. Grammaticos, A. Ramani, C. -M. Viallet
We present classes of discrete reversible systems which are at the same time chaotic and solvable.