The mathematical legacy of Andrzej Lasota

• Autorzy: Mackey M.C. , Tyran-Kamińska M. , Walther H. O.
• Konferencja: 6th European Congress of Mathematics, 2-7 July 2012 Kraków
• Języki publikacji: EN

Słowa kluczowe

EN

Lasota Andrzej; mathematical work

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2012
• Tom: T. 48, Nr 2
• Strony: 143--156
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Mackey M.C.

• Centre for Applied Mathematics in Bioscience and Medicine Departments of Physiology Physics & Mathematics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, CANADA, H3G 1Y6

autor

Tyran-Kamińska M.

• Institute of Mathematics University of Silesia, Bankowa 14, 40-007 Katowice Poland

autor

Walther H. O.

• Mathematisches Institut Universität Giessen Arndtstr. 2, 35392 Giessen, Germany

Bibliografia

• [1] U. an der Heiden, H.-O. Walther, Existence of chaos in control systems with delayed feedback,]. Differential Equations 47 (1983), 273-295.
• [2] J. Auslander, J. A. Yorke, Interval maps, factors of maps, and chaos, Tóhoku Math. J. 32 (1980), 177-188.
• [3] V. Baladi, Positive Transfer Operators and Decay of Correlations, Advanced Series in Nonlinear Dynamics, vol. 16, World Scientific Publishing Co. Inc., River Edge, NJ 2000.
• [4] P. Brunovsky, Notes on chaos in the cell population partial differential equation, Nonlinear Anal. 7 (1983), 167-176.
• [5] P. Brunovsky, J. Komornik, Ergodicity and exactness of the shift on C[0,∞] and the semiflow of a first-order partial differential equation, J. Math. Anal. Appl. 104 (1984), 235-245.
• [6] S.N. Chow, Existence of periodic solutions of autonomous functional differential equations, J. Differential Equations 15 (1974), 350-378.
• [7] O. Diekmann, S. A. van Gils, S. M. Verduyn Lunel, H.-O. Walther, Delay Equations: Functional-, Complex- and Nonlinear Analysis, Applied Mathematical Sciences, vol. 110, Springer-Verlag, New York 1995.
• [8] J. K. Hale, S. M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York 1993.
• [9] K. B. Hannsgen, J. J, Tyson, Stability of the steady-state size distribution in a model of cell growth and division, J. Math. Biol. 22 (1985), Z93-301.
• [10] G. Keller, Stochastic stability in some chaotic dynamical systems, Monatsh. Math. 94 (1982), 313-333.
• [11] G. Keller, C. Liverani, Stability of the spectrum for transfer operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999), 141-152.
• [12] J. Komornik, Asymptotic periodicity of Markov and related operators, in: Dynamics reported, Dynam. Report. Expositions Dynam. Systems (N.S.), vol. 2,1993, 31-68.
• [13] J. Komornik, A. Lasota, Asymptotic decomposition of Markov operators, Bull. Polish Acad. Sci. Math. 35 (1987), 321-327.
• [14] K. Krzyżewski, W. Szlenk, On invariant measures for expanding differentiate mappings, Studia Math. 33 (1969), 83-92
• [15] B. Lani-Wayda, Erratic solutions of simple delay equations, Trans. Amer. Math. Soc. 351 (1999), 901-945.
• [16] B. Lani-Wayda, H.-O. Walther, Chaotic motion generated by delayed negative feedback. Part I: A transversality criterion, Differential Integral Equations 8 (1995), 1407-1452.
• [17] B. Lani-Wayda, H.-O. Walther, Chaotic motion generated by delayed negative feedback. Part II: Construction of nonlinearities, Math. Nachr. 180 (1996), 141-211.
• [18] A. Lasota, Ergodic problems in biology, in: Dynamical systems. Vol. II - Warsaw, Asterisque, No. 50, 1977, 239-250.
• [19] A. Lasota, Invariant measures and a linear model of turbulence, Rend. Sem. Mat. Univ. Padova 61 (1979), 39-48.
• [20] A. Lasota, Stable and chaotic solutions of a first order partial differential equation, Nonlinear Anal. 5 (1981), no.11, 1181-1193.
• [21] A. Lasota, T.-Y. Li, J. A. Yorke, Asymptotic periodicity of the iterates of Markov operators, Trans. Amer. Math. Soc. 286 (1984), 751-764.
• [22] A. Lasota, M. C. Mackey, Globally asymptotic properties of proliferating cell populations,}. Math. Biol. 19 (1984), 43-62.
• [23] A. Lasota, M. C. Mackey, Chaos, fractals, and noise, Applied Mathematical Sciences, vol. 97, Springer-Verlag, New York 1994.
• [24] A. Lasota, M. C. Mackey, J. Tyrcha, The statistical dynamics of recurrent biological events, J. Math. Biol. 30 (1992), 775-800.
• [25] A. Lasota, M. C. Mackey, M. Ważewska-Czyżewska, Minimizing therapeutically induced anemia,]. Math. Biol. 13 (1981/82), 149-158.
• [26] A. LćłMjtu, J, A. Vorkfi. On the existence of invariant measures for piecewise mono-tonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481 488.
• [27] A. Lasota, J. A. Yorke, On the existence of invariant measures for transformations with strictly turbulent trajectories, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 25 (1977), 233-238.
• [28] A. Lasota, J, A. Yorke, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375-384.
• [29] J. Losson, M. C. Mackey, Coupled map lattices as models of deterministic and stochastic differential delay equations, Phys. Rev. E 52 (1995), 115-128.
• [30] M. C. Mackey, L. Glass, Oscillation and chaos in physiological control systems, Science 197 (1977), 287-289.
• [31] R. Rudnicki, Invariant measures for the flow of a first order partial differential equation, Ergodic Theory Dynam. Systems 5 (1985), 437-443.
• [32] R. Rudnicki, Strong ergodic properties of a first-order partial differential equation, J. Math. Anal. Appl. 133 (1988), 14-26.
• [33] R. Rudnicki, K. Pichór, M. Tyran-Kamińska, Markov semigroups and their applications, in: Dynamics of Dissipation, Lectures Notes in Physics, vol. 597, 2002, 215-238.
• [34] J. Tyrcha, Asymptotic stability in a generalized probabilistic/deterministic model of the cell cycle, J. Math. Biol. 26 (1988), 465-475.
• [35] M. Ważewska-Czyżewska, A. Lasota, Mathematical problems of the dynamics of a system of red blood cells, Mat. Stos. 6 (1976), 23-40.