ISSN:
0219-3094
Keywords:
82A68
;
82A69
;
14E05
;
14J50
;
16A46
;
16A24
;
functional relations
;
inversion relations
;
Yang-Baxter equations
;
rational dynamical zeta functions
;
discrete dynamical systems
;
birational mappings
;
Cremona transformations
;
analyticity assumptions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We recall some non-trivial, non-linear functional relations appearing in various domains of mathematics and physics, such as lattice statistical mechanics, quantum mechanics, or enumerative combinatorics. We focus, more particularly, on the analyticity properties of the solutions of these functional relations. We then consider discrete dynamical systems corresponding to birational transformations. The rational expressions for dynamical zeta functions obtained for a particular two-dimensional birational mapping, depending on two parameters, are recalled, as well as some non-trivial functional relations satisfied by these dynamical zeta functions. We finally give some functional equations corresponding to some singled out orbits of this two-dimensional birational mapping for particular values of the two parameters. This example shows that functional equations associated with curves, for real values of the variables, are actually compatible with a chaotic dynamical system.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01608780
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