We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations.
Hone, A.N.W., Ragnisco, O., Zullo, F. (2015). Algebraic entropy for algebraic maps. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 49(2), 02LT01 [10.1088/1751-8113/49/2/02LT01].
Algebraic entropy for algebraic maps
RAGNISCO, Orlando;
2015-01-01
Abstract
We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations.File in questo prodotto:
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