# Ergodic theory approach to chaos: Remarks and computational aspects

Paweł J. Mitkowski; Wojciech Mitkowski

International Journal of Applied Mathematics and Computer Science (2012)

- Volume: 22, Issue: 2, page 259-267
- ISSN: 1641-876X

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topPaweł J. Mitkowski, and Wojciech Mitkowski. "Ergodic theory approach to chaos: Remarks and computational aspects." International Journal of Applied Mathematics and Computer Science 22.2 (2012): 259-267. <http://eudml.org/doc/208106>.

@article{PawełJ2012,

abstract = {We 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.},

author = {Paweł J. Mitkowski, Wojciech Mitkowski},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {ergodic theory; chaos; invariant measures; attractors; delay differential equations},

language = {eng},

number = {2},

pages = {259-267},

title = {Ergodic theory approach to chaos: Remarks and computational aspects},

url = {http://eudml.org/doc/208106},

volume = {22},

year = {2012},

}

TY - JOUR

AU - Paweł J. Mitkowski

AU - Wojciech Mitkowski

TI - Ergodic theory approach to chaos: Remarks and computational aspects

JO - International Journal of Applied Mathematics and Computer Science

PY - 2012

VL - 22

IS - 2

SP - 259

EP - 267

AB - We 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.

LA - eng

KW - ergodic theory; chaos; invariant measures; attractors; delay differential equations

UR - http://eudml.org/doc/208106

ER -

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