INFINITE-DIMENSIONAL GENERALIZED CONTINUED FRACTIONS, DISTRIBUTION OF QUADRATIC RESIDUES AND NON-RESIDUES, AND ERGODIC THEORY

2002 ◽  
Vol 05 (04) ◽  
pp. 555-570
Author(s):  
L. D. PUSTYL'NIKOV
Keyword(s):  
Prime Number ◽  
Ergodic Theory ◽  
Continued Fractions ◽  
Classical Problem ◽  
Infinite Dimensional ◽  
Ergodic Properties ◽  
Quadratic Residues ◽  
Generalized Continued Fractions

A new theory of generalized continued fractions for infinite-dimensional vectors with integer components is constructed. The results of this theory are applied to the classical problem on the distribution of quadratic residues and non-residues modulo a prime number and are based on the study of ergodic properties of some infinite-dimensional transformations.

scholarly journals Ergodic theory approach to chaos: Remarks and computational aspects

2012 ◽  
Vol 22 (2) ◽  
pp. 259-267 ◽  
Author(s):  
Paweł Mitkowski ◽  
Wojciech Mitkowski
Keyword(s):  
Ergodic Theory ◽  
Computational Analysis ◽  
Theory Approach ◽  
Dimensional Model ◽  
Infinite Dimensional ◽  
Ergodic Properties ◽  
Computational Aspects ◽  
Characteristic Features ◽  
Delay Differential ◽  
Mixing Behaviour

Ergodic theory approach to chaos: Remarks and computational aspectsWe discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a nonsimple structure, supporting an invariant mixing measure. This observation verifies Lasota's conjecture concerning nontrivial ergodic properties of the model.

Markov chains and generalized continued fractions

1992 ◽  
Vol 29 (04) ◽  
pp. 838-849 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Wide Class ◽  
Stochastic Models ◽  
Continuous Time ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Continuous Time Markov Chains ◽  
Generalized Continued Fractions

This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.

Odometer actions on G-measures

1991 ◽  
Vol 11 (2) ◽  
pp. 279-307 ◽  
Author(s):  
Gavin Brown ◽  
Anthony H. Dooley
Keyword(s):  
Harmonic Analysis ◽  
Ergodic Theory ◽  
Finite Groups ◽  
Riesz Product ◽  
Direct Sum ◽  
New Methods ◽  
Product Construction ◽  
Ergodic Properties ◽  
Systematic Development

AbstractThe introduction of results from harmonic analysis leads to new methods in the study of the ergodic properties of measures under the action of the direct sum of finite groups. We take the first steps in a systematic development of part of ergodic theory based on the formalism of the Riesz product construction.

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