Ergodic theory approach to chaos: Remarks and computational aspects
By: Paweł Mitkowski and Wojciech Mitkowski
Open Access
|Jun 2012References
- Anosov, D. V. (1963). Ergodic properties of geodesic flows on closed Riemanian manifolds of negative curvature,: 1153-1156.
- Arnold, V. I. (1989)., 2nd Edn., Springer-Verlag, New York, NY, (translation from Russian).
- Auslander, J. and Yorke, J. A. (1980). Interval maps, factors of maps and chaos.: 177-188.
- Bass, J. (1974). Stationary functions and their applications to the theory of turbulence,: 354-399.
- Birkhoff, G. D. (1931a). Proof of a recurrence theorem for strongly transitive systems,: 650-655.
- Birkhoff, G. D. (1931b). Proof of the ergodic theorem,: 656-660.
- Birkhoff, G. D. and Koopman, B. O. (1932). Recent contributions to the ergodic theory,: 279-282.
- Bronsztejn, I. N., Siemiendiajew, K. A., Musiol, G. and Muhlig, H. (2004)., PWN, Warsaw, (in Polish, translation from German).
- Dawidowicz, A. L. (1992). On invariant measures supported on the compact sets II,: 25-28.
- Dawidowicz, A. L. (1992). A method of construction of an invariant measure,(3): 205-208.
- Dawidowicz, A. L. (2007). On the Avez method and its generalizations,: 46-55, (in Polish).
- Dawidowicz, A. L., Haribash, N. and Poskrobko, A. (2007). On the invariant measure for the quasi-linear Lasota equation.: 779-787.
- Devaney, R. L. (1987)., Addison-Wesley Publishing Company, New York, NY.
- Dorfman, J. R. (2001)., PWN, Warsaw, (in Polish, translation from English).
- Foias, C. (1973). Statistical study of Navier-Stokes equations II,: 9-123.
- Fomin, S. W., Kornfeld, I. P. and Sinaj, J. G. (1987)., PWN, Warsaw, (in Polish, translation from Russian).
- Górnicki, J. (2001). Fundamentals of nonlinear ergodic theory,: 5-16, (in Polish).
- Gurney, W. S. C., Blythe, S. P. and Nisbet, R. M. (1980). Nicholson's blowflies revisited,: 17-21.
- Kudrewicz, J. (1991)., WNT, Warsaw, (in Polish).
- Kudrewicz, J. (1993, 2007)., WNT, Warsaw, (in Polish).
- Landau, L. D., Lifszyc, J. M. (2007)., PWN, Warsaw, (in Polish, translation from Russian).
- de Larminat, P. and Thomas, Y. (1983)., WNT, Warsaw, (in Polish, translation from French).
- Lasota, A. (1977). Ergodic problems in biology,: 239-250.
- Lasota, A. (1979). Invariant measures and a linear model of turbulence,: 39-48.
- Lasota, A. (1981). Stable and chaotic solutions of a first order partial differential equation,(11): 1181-1193.
- Lasota, A. and Mackey, M. C. (1994)., Springer-Verlag, New York, NY.
- Lasota, A., Mackey, M. C. and Wazewska-Czyzewska, M. (1981). Minimazing theraupetically induced anemia,: 149-158.
- Lasota, A. and Myjak, J. (2002). On a dimension of measures,(2): 221-235.
- Lasota, A. and Szarek, T. (2002). Dimension of measures invariant with respect to the Wazewska partial differential equation,: 448-465.
- Lasota, A. and Yorke, J. A. (1973). On the existence of invariant measures for piecewise monotonic transformations,: 481-488.
- Lasota, A., and Yorke, J. A. (1977). On the existence of invariant measures for transformations with strictly turbulent trajectories,(3): 233-238.
- Lebowitz, J. L. and Penrose, O. (1973). Modern ergodic theory,: 155-175.
- Liz, E. and Rost, G. (2009). On the global attractor of delay differential equations with unimodal feedback,(4): 1215-1224.
- Mackey, M. C. (2007). Adventures in Poland: Having fun and doing research with Andrzej Lasota,: 5-32.
- Mackey, M. C. and Glass, L. (1977). Oscillations and chaos in physiological control systems,(4300): 287-289.
- Mitkowski, P. J. (2010). Numerical analysis of existence of invariant and ergodic measure in the model of dynamics of red blood cell's production system,, pp. 1-2.
- Mitkowski, P. J. (2011)., Ph.D. thesis, AGH University of Science and Technology, Cracow.
- Mitkowski, W. (2010). Chaos in linear systems,(5): 381-384, (in Polish).
- Mitkowski, P. J. and Ogorzałek, M. J. (2010). Ergodic properties of the model of dynamics of blood-forming system,, pp. 71-74.
- Myjak, J. (2008). Andrzej Lasota's selected results.(4): 363-394.
- Myjak, J. and Rudnicki, R. (2002). Stability versus chaos for a partial differential equation,: 607-612.
- Nadzieja, T. (1996). Individual ergodic theorem from the topological point of view,: 27-36, (in Polish).
- Nicholson, A. J. (1954). An outline of the dynamic of animal population,: 9-65.
- Ott, E. (1993)., WNT, Warsaw, (in Polish, translation from English).
- Prodi, G. (1960)., C. I. M. E., Rome.
- Rudnicki, R. (1985a). Invariant measures for the flow of a first order partial differential equation,: 437-443.
- Rudnicki, R. (1985b). Ergodic properties of hyperbolic systems of partial differential equations,(11-12): 595-599.
- Rudnicki, R. (1988). Strong ergodic properties of a first-order partial differential equation,: 14-26.
- Rudnicki, R. (2004). Chaos for some infinite-dimensional dynamical systems,: 723-738.
- Rudnicki, R. (2009). Chaoticity of the blood cell production system,(043112): 1-6.
- Shampine, L. F., Thompson, S. and Kierzenka, J. (2002). Solving delay differential equations with dde23, available at
- Silva, C. E. (2010). Lecture on dynamical systems,
- Szlenk, W. (1982)., PWN, Warsaw, (in Polish).
- Taylor, S. R. (2004),, Ph.D. thesis, University of Waterloo, Ontario, Canada.
- Tucker, W. (1999). The Lorenz attractor exists,(I): 1197-1202.
- Ulam, S. M. (1960),, Interscience Publishers, New York, NY/London.
- Walther, H. O. (1981). Homoclinic solution and chaos in() =((- 1)),(7): 775-788.
- Ważewska-Czyżewska, M. (1983)., National Center for Scientific, Technical and Economic Information, Warsaw.
- Ważewska-Czyżewska, M. and Lasota, A. (1976). Mathematical problems of blood cells dynamics system,: 23-40, (in Polish).
Language: English
Page range: 259 - 267
Published on: Jun 28, 2012
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Related subjects:
© 2012 Paweł Mitkowski, Wojciech Mitkowski, published by University of Zielona Góra
This work is licensed under the Creative Commons License.