Chaotyczne liniowe układy dynamiczne : teoria i zastosowanie

• Autorzy: Banasiak J.
• Języki publikacji: PL

Słowa kluczowe

PL

chaos; układ dynamiczny; liniowy układ dynamiczny; przestrzenie Banacha

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
• Rocznik: 2005
• Tom: [Z] 41
• Strony: 51--79
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Banasiak J.

• School of Mathematical and Statistical Sciences, University of Natal, Durban 4041, South Africa
• Instytut Matematyki Politechniki Łódzkiej, al. Politechniki 11, 90-924 Łódź, Polska

Bibliografia

• [1] J. Banasiak, Birth-and-death type systems with parameter and chaotic dynamics of some linear kinetic models, Z. Anal. Anwendungen, 24 (2005), 675-690.
• [2] J. Banasiak, An introduction to chaotic linear systems, School of Mathematical and Statistical Sciences, University of Natal, Internal Report 3 (2001), http://duck.cs.und.ac.za/~banasiak/reports.html.
• [3] J. Banasiak, G. Frosali, G. Spiga, Asymptotic Analysis for a Particle Transport Equation with Inelastic Scattering in Extended Kinetic Theory, Math. Models Methods Appl. Sci., 8 5, (1998), 851-874.
• [4] J. Banasiak and M. Lachowicz, Chaos for a class of linear kinetic models, Compt. Rend. Acad. Sci. Paris, 329, ser. II b, (2001), 439-444.
• [5] J. Banasiak and M. Lachowicz, Topological chaos for birth-and-death-type models with proliferation, Math. Models Methods Appl. Sci., 12 (2002), 755-775.
• [6] J. Banasiak, M. Lachowicz, M. Moszyński, Topological Chaos: When Topology Meets Medicine, Appl. Math. Lett., 16 (2003), 303-308.
• [7] J. Banasiak, M. Moszyński, A generalization of Desch-Schappacher-Webb criteria for chaos, Discrete Contin. Dyn. Syst. -A, 12, (2005), 959-972.
• [8] J. Banasiak, M. Lachowicz, M. Moszyński, Chaotic behavior of semigroups related to the process of gene amplification-deamplification with cells’ proliferation, Math. Biosci., 199 (2006) (przyjęta do druku), również dostępna jako: Technical report of the Institute of Applied Mathematics and Mechanics 145/2004, http://www.mimuw.edu.pl/english/research/reports/imsm/).
• [9] J. Banasiak, M. Lachowicz, M. Moszyński, Semigroups for generalized birth-and-death equations in lp spaces, złożona do druku, (również dostępna jako: Technical report of the Institute of Applied Mathematics and Mechanics 149/2005, http: //www.mimuw.edu.pl/english/research/reports/imsm/).
• [10] J. Banks, J. Brooks, G. Cairns, G. Davis, P. Stacey, On Devaney’s definition of chaos, Amer. Math. Monthly, 99 (1992), 332-334.
• [11] R. de Laubenfels, H. Emamirad, Chaos for functions of discrete and continuous weighted shift operators, Ergod. Th. & Dynam. Systems, 21 (2001), 1411-1427.
• [12] W. Desch, W. Schappacher, G. F. Webb, Hypercyclic and chaotic semigroups of linear operators, Ergod. Th. & Dynam. Systems, 17 (1997), 793-819.
• [13] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd edn., Addison-Wesley, NY, 1989.
• [14] J.-P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Modern Phys., 57 (1985), 617-656.
• [15] G. Godefroy, J. H. Shapiro, Operators with dense, invariant, cyclic manifolds, J. Funct. Anal., 98 (1991), 229-269.
• [16] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985.
• [17] D. A. Herrero, Hypercyclic operators and chaos, J. Operator Theory, 28 (1992), 93-103.
• [18] D. A. Hill, Chaotic chaos, Math. Intelligencer, 22 (2000), 5.
• [19] E. Hille, R. S. Phillips, Functional Analysis and Semi-groups, Colloquium Publications, v. 31, American Mathematical Society, Providence, 1957.
• [20] M. Kimmel, A. Świerniak and A. Polański, Infinite-dimensional model of evolution of drug resistance of cancer cells, J. Math. Systems Estimation Control, 8 (1998), 1-16.
• [21] A. Lasota, M. C. Mackey, Chaos, Fractals and Noise, Stochastics Aspects of Dynamics, Springer Verlag, New York, 1995.
• [22] E. N. Lorenz, Deterministic nonperiodic flow, J. Atmosph. Sci., 20 (1963), 130-141.
• [23] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
• [24] V. Protopopescu, Y. Y. Azmy, Topological chaos for a class of linear models, Math. Models Methods Appl. Sci., 2 (1992), 79-90.
• [25] R. Rudnicki, Invariant measures for the flow of a first-order partial differential equation, Ergod. Th. & Dynam. Systems, 5 (1985), 437-443.
• [26] R. Rudnicki, Strong ergodic properties of a first-order partial differential equation, J. Math. Anal. Appl., 133 (1988), 14-26.
• [27] R. Rudnicki, Chaos for some infinite-dimensional dynamical systems, Math. Meth. Appl. Sci., 27 (2004), 723-736.
• [28] D. Ruelle, F. Takens, On the nature of turbulence, Comm. Math. Phys., 20 (1973), 167-192.
• [29] W. Tucker, The Lorenz attractor exists, Compt. Rend. Acad. Sci. Paris, 328, ser. I (1999), 1197-1202.
• [30] M. Viana, What’s New on Lorenz Strange Attractors?, Math. Intelligencer, 22 (2000), 6-19.
• [31] G. F. Webb, Periodic and chaotic behavior in structured models of cell population dynamics, in: A. C. McBride, G. F. Roach (Eds.) Recent developments in evolution equations, Pitman Research Notes in Mathematics 134, Longman Scientific & Technical, Harlow, 1995, 40-49.