Kooperativer Bibliotheksverbund

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Format: 1 online resource (475 pages)

Edition: 1st ed.

ISBN: 9783031600579

Note: Intro -- Preface -- Contents -- Notation -- 1 Poisson Stable Motions of Dynamical Systems -- 1.1 Introduction -- 1.2 Some Notions, Notation, and Facts from the Theory of Dynamical Systems -- 1.3 Minimal Sets and Recurrent Motions -- 1.3.1 Minimal Sets -- 1.3.2 Almost Recurrent Motions -- 1.3.3 Recurrent Motions -- 1.4 Lyapunov Stable Sets -- 1.5 Almost Periodic Motions -- 1.6 Comparability by the Character of Recurrence of Motions for Dynamical Systems -- 1.6.1 B. A. Shcherbakov's Principle of Comparability of Motions by Their Character of Recurrence -- 1.6.2 Some Generalization of B. A. Shcherbakov's Results -- 1.6.3 Strongly Comparability of Motions by Their Character of Recurrence -- 1.7 Asymptotically Almost Periodic Motions -- 1.7.1 Asymptotically Poisson Stable Motions -- 1.7.2 Criterion of Asymptotical Almost Periodicity -- 1.7.3 Asymptotically Periodic Motions -- 1.7.4 Comparability by the Character of Recurrence in the Limit of Asymptotically Poisson Stable Motions -- 1.8 Almost Periodic and Asymptotically Almost Periodic Functions -- 1.8.1 Bohr Almost Periodic Functions -- 1.8.2 Levitan Almost Periodic Functions -- 1.8.3 Fréchet Asymptotically Almost Periodic Functions -- 2 Compact Global Attractors -- 2.1 Introduction -- 2.2 Limit Properties of Dynamical Systems -- 2.3 Levinson Center -- 2.4 Dissipative Systems on the Local Compact Spaces -- 2.5 Criterions of Compact Dissipativity -- 2.6 Global Attractor of Nonautonomous Dynamical Systems -- 2.6.1 Nonautonomous Sets -- 2.6.2 Maximal Compact Invariant Sets -- 2.7 Pullback Attractors of Cocycles -- 2.8 Global Attractors of Cocycles -- 2.9 Forward Attractors for Cocycles -- 3 V-Monotone Nonautonomous Dynamical Systems -- 3.1 Introduction -- 3.2 Global Attractors of V-Monotone NDS -- 3.3 On the Structure of Levinson Center of V-Monotone NDS. , 3.4 Almost Periodic Solutions of V-Monotone Systems -- 3.5 Pullback Attractors of V-Monotone NDS -- 3.6 Applications -- 3.6.1 Finite-Dimensional Systems -- 3.6.2 Caratheodory`s Differential Equations -- 3.6.3 ODEs with Impulse -- 3.6.4 Evolution Equations with Monotone Operators -- 3.7 Continuous Invariant Sections of NDS -- 3.7.1 Contraction Principle and Its Generalizations -- 3.7.2 Invariant Sections of NDS -- 3.7.3 Global Attractors of V-monotone NDS -- 3.7.4 Bohr/Levitan Almost Periodic Motions of V-Monotone NDS -- 3.7.5 Applications -- Finite-Dimensional Systems -- Caratheodory's Differential Equations -- ODEs with Impulse -- ODEs in Banach Spaces -- Evolution Equations with Monotone Operators -- 3.8 Second Order Monotone Equations in the Hilbert Spaces -- 3.8.1 Some NDS Generated by Differential Equations in the Banach Spaces -- 3.8.2 Invariant Sections of Second Order Differential Equations -- Invariant Sections -- Linear Case -- Quasiperiodic Solutions -- Invariant Sections of Equation x''=V(x)+f(σ(t,y)) -- 3.8.3 Almost Automorphic Solutions of Monotone Second Order Differential Equation -- 4 Poisson Stable Motions and Global Attractors of Monotone Nonautonomous Dynamical Systems -- 4.1 Introduction -- 4.2 Poisson Stable Motions of Monotone NDS -- 4.2.1 Structure of the ω-Limit Set -- 4.2.2 Comparable Motions by Character of their Recurrence for Monotone NDS -- 4.2.3 Applications -- Ordinary Differential Equations -- Functional Differential Equations with Finite Delay -- Parabolic Systems -- 4.3 I. U. Bronshtein's Conjecture for Monotone NDS -- 4.3.1 I. U. Bronshtein's Conjecture for Cocycles -- 4.3.2 Applications -- Dissipative Cocycles -- Ordinary Differential Equations -- Difference Equations -- 4.4 Structure of the Levinson Center for Monotone NDS -- 4.5 Applications -- 4.5.1 Ordinary Differential Equations. , Scalar Differential Equations -- 4.5.2 Difference Equations -- 4.5.3 Functional Differential Equations with Finite Delay -- 4.5.4 Parabolic Systems -- 5 One-Dimensional Monotone Nonautonomous Dynamical Systems -- 5.1 Introduction -- 5.2 One-Dimensional Monotone Differential/Difference Equations -- 5.3 Invariant Sets -- 5.4 Structure of Levinson Center for One-Dimensional Monotone Cocycles -- 5.5 Pinched Sets -- 5.6 Minimal Sets of One-Dimensional Monotone Cocycles -- 5.7 Applications -- 5.7.1 Scalar Differential Equations -- 5.7.2 Scalar Difference Equations -- 5.8 Bohr/Levitan Almost Periodic Solutions of Scalar Differential Equations -- 5.8.1 Some Criterion of the Existence of Fixed Point for a Semigroup of Transformations -- 5.8.2 Distal NDS with the Minimal Base -- 5.8.3 Structure of the ω-Limit Set -- 5.8.4 Scalar Differential Equations -- 5.9 Bohr/Levitan Almost Periodic Solutions of the Second Order Differential Equation -- 5.9.1 Some Nonautonomous Dynamical Systems Generated by the Second Order Differential Equations -- 5.9.2 Levitan Almost Periodic and Almost Automorphic Solutions of the Second Order Differential Equations -- 5.9.3 Quasiperiodic, Bohr/Levitan Almost Periodic, and Recurrent Solutions of the Second Order Differential Equations -- 5.9.4 Some Generalizations -- 6 Monotone Nonautonomous Dynamical Systems with a First Integral -- 6.1 Introduction -- 6.2 Convergence in NDS with a Strictly Monotone First Integral -- 6.3 Asymptotically Almost Periodic Motions of NDS with a First Integral -- 6.4 Applications -- 6.4.1 Ordinary Differential Equations -- 6.4.2 Linear Differential Equations -- 6.4.3 Linear Differential Equations with Constant Matrix -- 6.4.4 Difference Equations -- 6.4.5 Linear Difference Equations -- 6.4.6 Perron-Frobenius Dynamics -- 6.5 Levinson Center for Monotone NDS with a Strictly Monotone First Integral. , 6.6 Applications -- 6.6.1 Nonlinear Differential Equations -- 6.6.2 Linear Differential Equations -- 6.6.3 Difference Equations -- 6.6.4 Linear Difference Equations -- 7 Monotone Sub-Linear Nonautonomous Dynamical Systems -- 7.1 Introduction -- 7.2 Existence and Convergence to Poisson Stable Motions of Monotone NDSs -- 7.3 Uniformly Stable Monotone Nonautonomous Dynamical Systems -- 7.4 Sub-Linear Nonautonomous Dynamical Systems -- 7.5 Comparability by the Character of Recurrence of Motions for Sub-Linear Cocycles -- 7.6 Application -- 7.6.1 Ordinary Differential Equations -- 7.6.2 Functional Differential Equations with Finite Delay -- 7.6.3 Difference Equations -- 7.7 Translation-Invariant Monotone Systems -- 7.8 Time-Dependent Chemical Reaction Networks -- 7.9 Translation-Invariant Discrete Monotone Systems -- Bibliography -- Index.

Additional Edition: ISBN 9783031600562

Language: English