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Continuous separation for monotone skew-product semiflows: From theoretical to numerical results
Belitskii--Lyubich conjecture for $C$-analytic dynamical systems
1. | State University of Moldova, Department of Mathematics and Informatics, A. Mateevich Street 60, MD–2009 Chişinău |
References:
[1] |
R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii, Measures of Noncompactness and Condensing Operators, Translated from the 1986 Russian original by A. Iacob, Operator Theory: Advances and Applications, 55, Birkhäuser Verlag, Basel, 1992.
doi: 10.1007/978-3-0348-5727-7. |
[2] |
G. R. Belitskii and Yu. I. Lyubich, Matrix norms and their applications, Operator Theory: Advances and Applications, 36, Birkhäuser Verlag, Basel, 1988.
doi: 10.1007/978-3-0348-7400-7. |
[3] |
D. N. Cheban, Global Attractors of Non-Autonomous Dissipstive Dynamical Systems, Interdisciplinary Mathematical Sciences, 1, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2004.
doi: 10.1142/9789812563088. |
[4] |
D. N. Cheban, Markus-Yamabe conjecture, in Communications, The 14-th Conference of Applied and Industrial Mathematics, Chisinau, 2006, 107-110. |
[5] |
D. N. Cheban, Lyapunov Stability of Non-Autonomous Dynamical Systems, Nova Science Publishers Inc., New York, 2013. |
[6] |
D. N. Cheban and C. Mammana, Absolute asymptotic stability of discrete linear inclusions, Bul. Acad. Ştiinţe Repub. Mold. Mat., (2005), 43-68. |
[7] |
G. Darbo, Punti uniti in transformazioni non-compacto, Rend. Sem. Mat. Univ. Padova, 24 (1955), 84-92. |
[8] |
C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, in Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., (1968)), American Mathematical Society, Rhode Island, 1970, 61-65. |
[9] |
J. K. Hale, Asymptotic Behaviour of Dissipative Systems, Amer. Math. Soc., Providence, RI, 1988. |
[10] |
J. K. Hale and O. Lopes, Fixed point theorems and dissipative processes, Journal of Differential Equations, 13 (1973), 391-402.
doi: 10.1016/0022-0396(73)90025-9. |
[11] |
A. Halanay and D. Wexler, Teoria Calitativă a Sistemelor cu Impulsuri, Bucureşti, 1968. |
[12] |
L. A. Harris, Fixed points of holomorphic mappings for domains in Banach spaces, Abstract and Applied Analysis, (2003), 261-274.
doi: 10.1155/S1085337503205042. |
[13] |
G. S. Jones, The existence of critical points in generalized dynamical systems, in Seminaire on Differential Equations and Dynamical Systems, Lecture Notes in Math., Springer, Berlin, 1968, 7-19. |
[14] |
O. A. Ladyzhenskaya, Finding minimal global attractors for Navier-Stokes equations and other partial differential equations, Uspekhi Mat. Nauk, 42 (1987), 25-60, 246; English translation: Russian Math. Surveys, 42 (1987), 27-73. |
[15] |
J. Mujica, Complex Analysis in Banach Spaces. Holomorphic Functions and Domains of Holomorphy in Finite and Infinite Dimensions, North-Holland Mathematics Studies, 120, North-Holland Publishing Co., Amsterdam, 1986. |
[16] |
Z. Nitecki, Differentiable Dynamics, The MIT Press, Cambridge, Mass.-London, 1971. |
[17] |
V. I. Opoitsev, A converse of the contraction mapping principle, Uspehi Mat. Nauk, 31 (1976), 169-198. |
[18] |
B. N. Sadovskii, About one fixed point principle, (in Russian) Functional Analysis and Applications, 1 (1967), 74-76; English translation: Functional Analysis and Its Applications, 1 (1967), 151-153. |
[19] |
B. N. Sadovskii, Limit-compact and condensing operators, (in Russian) Uspehi Mat. Nauk, 27 (1972), 81-146; English translation: Russian Mathematical Surveys, 27 (1972), 85-155. |
[20] |
V. E. Slyusarchuk, Counterexample to a conjecture on smooth mappings, Russian Mathematical Surveys, 53 (1998), 408-409.
doi: 10.1070/rm1998v053n02ABEH000046. |
[21] |
M.-H. Shih and J.-W. Wu, Asymptotic stability in the Schauder fixed point theorem, Stud. Math., 131 (1998), 143-148. |
show all references
References:
[1] |
R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii, Measures of Noncompactness and Condensing Operators, Translated from the 1986 Russian original by A. Iacob, Operator Theory: Advances and Applications, 55, Birkhäuser Verlag, Basel, 1992.
doi: 10.1007/978-3-0348-5727-7. |
[2] |
G. R. Belitskii and Yu. I. Lyubich, Matrix norms and their applications, Operator Theory: Advances and Applications, 36, Birkhäuser Verlag, Basel, 1988.
doi: 10.1007/978-3-0348-7400-7. |
[3] |
D. N. Cheban, Global Attractors of Non-Autonomous Dissipstive Dynamical Systems, Interdisciplinary Mathematical Sciences, 1, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2004.
doi: 10.1142/9789812563088. |
[4] |
D. N. Cheban, Markus-Yamabe conjecture, in Communications, The 14-th Conference of Applied and Industrial Mathematics, Chisinau, 2006, 107-110. |
[5] |
D. N. Cheban, Lyapunov Stability of Non-Autonomous Dynamical Systems, Nova Science Publishers Inc., New York, 2013. |
[6] |
D. N. Cheban and C. Mammana, Absolute asymptotic stability of discrete linear inclusions, Bul. Acad. Ştiinţe Repub. Mold. Mat., (2005), 43-68. |
[7] |
G. Darbo, Punti uniti in transformazioni non-compacto, Rend. Sem. Mat. Univ. Padova, 24 (1955), 84-92. |
[8] |
C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, in Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., (1968)), American Mathematical Society, Rhode Island, 1970, 61-65. |
[9] |
J. K. Hale, Asymptotic Behaviour of Dissipative Systems, Amer. Math. Soc., Providence, RI, 1988. |
[10] |
J. K. Hale and O. Lopes, Fixed point theorems and dissipative processes, Journal of Differential Equations, 13 (1973), 391-402.
doi: 10.1016/0022-0396(73)90025-9. |
[11] |
A. Halanay and D. Wexler, Teoria Calitativă a Sistemelor cu Impulsuri, Bucureşti, 1968. |
[12] |
L. A. Harris, Fixed points of holomorphic mappings for domains in Banach spaces, Abstract and Applied Analysis, (2003), 261-274.
doi: 10.1155/S1085337503205042. |
[13] |
G. S. Jones, The existence of critical points in generalized dynamical systems, in Seminaire on Differential Equations and Dynamical Systems, Lecture Notes in Math., Springer, Berlin, 1968, 7-19. |
[14] |
O. A. Ladyzhenskaya, Finding minimal global attractors for Navier-Stokes equations and other partial differential equations, Uspekhi Mat. Nauk, 42 (1987), 25-60, 246; English translation: Russian Math. Surveys, 42 (1987), 27-73. |
[15] |
J. Mujica, Complex Analysis in Banach Spaces. Holomorphic Functions and Domains of Holomorphy in Finite and Infinite Dimensions, North-Holland Mathematics Studies, 120, North-Holland Publishing Co., Amsterdam, 1986. |
[16] |
Z. Nitecki, Differentiable Dynamics, The MIT Press, Cambridge, Mass.-London, 1971. |
[17] |
V. I. Opoitsev, A converse of the contraction mapping principle, Uspehi Mat. Nauk, 31 (1976), 169-198. |
[18] |
B. N. Sadovskii, About one fixed point principle, (in Russian) Functional Analysis and Applications, 1 (1967), 74-76; English translation: Functional Analysis and Its Applications, 1 (1967), 151-153. |
[19] |
B. N. Sadovskii, Limit-compact and condensing operators, (in Russian) Uspehi Mat. Nauk, 27 (1972), 81-146; English translation: Russian Mathematical Surveys, 27 (1972), 85-155. |
[20] |
V. E. Slyusarchuk, Counterexample to a conjecture on smooth mappings, Russian Mathematical Surveys, 53 (1998), 408-409.
doi: 10.1070/rm1998v053n02ABEH000046. |
[21] |
M.-H. Shih and J.-W. Wu, Asymptotic stability in the Schauder fixed point theorem, Stud. Math., 131 (1998), 143-148. |
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