Adventures in Poland: Having Fun and Doing Research with Andrzej Lasota

• Autorzy: Mackey M.C.
• Języki publikacji: EN

Abstrakty

EN

This is an account of my scientific and personal friendship with Prof. Andrzej (Andy) Aleksander Lasota from 1977 until his death 28 December, 2006. It is a tale that fascinates me because of the intertwined links between many people both East and West of several generations, and it illustrates what I feel is the strength and beauty of the personal side of the scientific endeavor.

Słowa kluczowe

EN

mathematical biology; Markov operator; dynamical system; Frobenius-Perron operators

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Matematyka Stosowana : matematyka dla społeczeństwa
• Rocznik: 2007
• Tom: Nr 8
• Strony: 5--32
• Opis fizyczny: bibliogr. 39 poz., fot.

Twórcy

autor

Mackey M.C.

• Departments of Physiology, Physics & Mathematics and Centre for Nonlinear Dynamics, McGill University, 3655 Promenade Sir William Osier, Montreal, QC, CANADA, H3G 1Y6,

Bibliografia

• [1] M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science 197:287-289, 1977.
• [2] A. Lasota and M. Ważewska-Czyżewska Matematyczne problemy dynamiki układu krwinek czerwonych (Mathematical problems of the dynamics of red blood cell population), (in Polish), Matematyka Stosowana (1976), 6:23-40.
• [3] S.-N. Chow, Existence of periodic solutions of autonomous functional differential equations, J. Diff. Eqn. (1974), 15:350-378.
• [4] J. D. Murray, Wprowadzenie do biomatematyki (translated by Urszula Foryś and Marek Bodnar), Wydawnictwo Naukowe PWN, Warsaw, 2007.
• [5] C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia, J. Theor. Biol. (2005) 237, 117-132.
• [6] A. Lasota, Ergodic problems in biology, Dynamical systems, Vol. II-Warsaw, pp. 239-250. Astérisque, No. 50, Soc. Math. France, Paris, 1977.
• [7] A. Lasota and M. C. Mackey, The extinction of slowly evolving dynamical systems J. Math. Biol. (1980) 10, 333-345.
• [8] M. C. Mackey and J. G. Milton, A deterministic approach to survival statistics, J. Math. Biol. (1990), 28(1), 33-48.
• [9] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, New York-Cambridge, 1985.
• [10] A. Lasota, M.C. Mackey and M. Ważewska-Czyżewska, Minimizing therapeutically induced anemia, J. Math. Biol. (1981) 13, 149-158.
• [11] J. Szarski, Differential inequalities, Monografie Matematyczne, Tom 43, PWN, Warsaw, 1965.
• [12] A. Lasota and M. C. Mackey, Globally asymptotic properties of proliferating cell populations, J. Math. Biol. (1984), 19, 43-62.
• [13] M. C. Mackey, M. Santavy and P. Selepova, A mitotic oscillator model for the cell cycle with a strange attractor, in Nonlinear Oscillations in Biology and Chemistry (ed. H. Othmer), Lecture Notes in Biomathematics, volume 66, 1986, pp. 34-45. Springer- Verlag, Berlin-Heidelberg-New York.
• [14] M. C. Mackey, Time's Arrow: The Origins of Thermodynamic Behaviour, Springer- Verlag, 1992.
• [15] J. Komornik and A. Lasota, Asymptotic decomposition of Markov operators, Bull. Polish. Acad. Sci. (Math.) (1987), 35, 321-327.
• [16] A. Lasota, T. Y. Li and J. A.Yorke, Asymptotic periodicity of the iterates of Markov operators, Trans. Amer. Math. Soc. (1984), 286, 751-764.
• [17] A. Lasota and M. C. Mackey, Noise and statistical periodicity, Physica (1987), 28D, 143-154.
• [18] N. Provatas and M. C. Mackey, Noise induced asymptotic periodicity in a piecewise linear map, J. Stat. Phys. (1991), 63, 661-688.
• [19] N. Provatas and M. C. Mackey, Asymptotic periodicity and banded chaos, Phys. D (1991), 53, 295-318.
• [20] A. Lasota and M. C. Mackey, Stochastic perturbation of dynamical systems: The weak convergence of measures, J. Math. Anal. and Applic. (1989), 138, 232-248.
• [21] D. Bohm, A suggested interpretation of quantum mechanics in terms of "hidden" variables: I, Phys. Rev., 1952, 85, 166-179.
• [22] J. Losson and M. C. Mackey, Statistical cycling in coupled map lattices, Phys. Rev. E. (1994), 50, 843-856.
• [23] A. Lasota, K. Łoskot and M. C. Mackey, The dynamics of proliferatively coupled cell populations, Acta Biotheor. (1991), 39, 1-14.
• [24] M. C. Mackey, A. Longtin and A. Lasota, Noise induced global asymptotic stability, J. Stat. Phys. (1990), 60, 735-751.
• [25] A. Lasota, M. C. Mackey and J. Tyrcha, The statistical dynamics of irregular biological events, J. Math. Biol. (1992), 30, 775-800.
• [26] A. Lasota and M. C. Mackey, Statistical stability of strongly perturbed dynamical systems, In Differential equations with applications to biology (Halifax, NS, 1997), volume 21 of Fields Inst. Commun., pages 363-376. Amer. Math. Soc., Providence, RI, 1999.
• [27] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Springer-Verlag, 1994.
• [28] A. Lasota and M. C. Mackey, Cell division and the stability of cellular populations, J. Math. Biol. (1999), 38, 241-261.
• [29] M. C. Mackey and R. Rudnicki, Global stability in a delayed partial differential equation describing cellular replication, J. Math. Biol. (1994), 33, 89-109.
• [30] R. Rudnicki and M. C. Mackey, Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations, J. Math. Anal. Applic. (1994), 187, 548-566.
• [31] M. C. Mackey and R. Rudnicki, A new criterion for the global stability of simultaneous cell replication and maturation processes, J. Math. Biol. (1999), 38, 195-219.
• [32] A. Lasota and J. Traple, Differential equations with dynamical perturbations, J.Diff. Eqns (1986), 63, 406-417.
• [33] M. C. Mackey and M. Tyran-Kamińska, Deterministic Brownian Motion: The effects of perturbing a dynamical system by a chaotic semi-dynamical system, Phys. Reports (2006), 422, 167-222.
• [34] M. C. Mackey and M. Tyran-Kamińska, Central limit theorem behavior in the skew tent map, Chaos, Solitons and Fractals (in press).
• [35] M. C. Mackey and M. Tyran-Kamińska, Central limit theorems for non-invertible measure preserving maps, Colloquium Mathematicum (in press).
• [36] M. C. Mackey and M. Tyran-Kamińska, Noise and conditional entropy evolution, Physica A (2006), 365, 360-382.
• [37] M. C. Mackey and M. Tyran-Kamińska, Temporal behavior of the conditional and Gibbs entropies, J. Stat. Phys. (2006), 124, 1443-1470.
• [38] A. Lasota, Determinism, indeterminism, and mathematics, Found. Sci. (1997), 2, 73-75.
• [39] J. Urbaniec, An interview with Andrzej Lasota: Without the physical world, there would be no mathematics either, Found. Sci. (1997), 2, 183-189.