Prigogine dynamical systems based on Bernoulli shifts of real functions

• Autores: Franz Pichler
• Localización: Revista de la Academia Canaria de Ciencias: = Folia Canariensis Academiae Scientiarum, ISSN 1130-4723, Vol. 11, Nº. 1-2, 1999, págs. 237-247
• Idioma: inglés
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• Resumen

  • The baker-transform and the related dynamical system is usually studied with the unit-square as its state-space. In this paper we define the bakertransform and related discrete-time dynamical system with the non-negative real numbers as state-space. Furthermore we consider the extension of the so defined baker transform to real-valued functions. As a mathematical instrument we use the generalized Walsh-Functions as originally introduced by Fine (1950). The A-transform of Prigogine is proven to be identical to dyadic convolution. It is shown that the method of Prigogine to construct irreversible processes can also in this case be applied successfully.