Preface -- Contents -- Notations -- Autonomous dynamical systems -- 1.1 Some notions, notations and facts from theory of dynamical systems -- 1.2 Limit properties of dynamical systems -- 1.3 Center of Levinson -- 1.4 Dissipative systems on the local compact spaces -- 1.5 Criterions of compact dissipativity -- 1.6 Local dissipative systems -- 1.7 Global attractors -- 1.8 On a Problem of J. Hale -- 1.9 Connectedness of the Levinson's center -- 1.10 Weak attractors and center of Levinson -- 1.11 Asymptotic stability -- Non-autonomous dissipative dynamical systems -- 2.1 On the stability of Levinson's center -- 2.2 The positively stable systems -- 2.3 Behaviour of dissipative dynamical systems under homomorphisms -- 2.4 Non-autonomous dynamical systems with convergence -- 2.5 Tests for convergence -- 2.6 Global attractors of non-autonomous dynamical systems -- 2.7 Global attractor of cocycles -- 2.8 Global attractors of non-autonomous dynamical system with minimal base -- 2.9 Homogeneous dynamical systems -- 2.10 Power-law asymptotic of homogeneous systems -- 2.11 Linear systems -- Analytic dissipative systems -- 3.1 Skew-product dynamical systems and cocycles -- 3.2 C-analytic systems -- 3.3 Converse of Lyapunov's theorem for C-analytic systems -- 3.4 On the structure of compact attracting sets of C-analytic systems -- 3.5 Dynamical systems in spaces of sections -- 3.6 Quasi-periodic solutions -- 3.7 The analogy of Cameron-Johnson's theorem -- 3.8 Almost periodic solutions of the weak nonlinear dissipative systems -- The structure of the Levinson center of system with the condition of the hyperbolicity -- 4.1 The chain recurrent motions -- 4.2 The spectral decomposition of the Levinson's center -- 4.3 One-dimensional systems with hyperbolic center -- 4.4 The dissipative cascades -- 4.5 The periodic dissipative systems -- Method of Lyapunov functions.

5.1 Criterions of dissipativity in term of Lyapunov functions -- 5.2 Some criterions of dissipativity of differential equations -- 5.3 Theorem of Barbashin{Krasovskii for non-autonomous dynamical systems -- 5.4 Equations with convergence -- 5.5 Dissipativity and convergence of some equations of 2nd and 3rd order -- 5.6 Construction of Lyapunov function for homogeneous systems -- 5.7 Differentiable homogeneous systems -- 5.8 Global attractors of quasi-homogeneous systems -- Dissipativity of some classes of equations -- 6.1 Difference equations -- 6.2 Equations with impulse -- 6.3 Convergent periodic equations with impulse -- 6.4 Asymptotic stability of linear functional differential equations -- 6.5 Convergence of monotone evolutionary equations -- 6.6 Global attractors of non-autonomous Lorenz systems -- 6.6.1 Non-autonomous Lorenz systems -- 6.6.2 Non-autonomous dissipative dynamical systems and their attractors -- 6.6.3 Almost periodic and recurrent solutions of non-autonomous Lorenz systems -- 6.6.4 Uniform averaging principle -- 6.6.5 Global averaging principle for the non-autonomous Lorenz 6.6.5 Global averaging principle for the non-autonomous Lorenz -- Upper semi-continuity of attractors -- 7.1 Introduction -- 7.2 Maximal compact invariant sets -- 7.3 Upper semi-continuity -- 7.4 Connectedness -- 7.5 Applications -- 7.5.1 Quasi-homogeneous systems -- 7.5.2 Monotone systems -- 7.5.3 Quasi-linear systems -- 7.5.4 Non-autonomously perturbed systems -- 7.5.5 Non-autonomous 2D Navier-Stokes equations -- 7.5.6 Quasi-linear functional-di erential equations -- The relationship between pullback, forward and global attractors -- 8.1 Pullback, forward and global attractors -- 8.2 Asymptotic stability in -condensing semi{dynamical systems -- 8.3 Uniform pullback attractors and global attractors -- 8.4 Examples of uniform pullback attractors.

8.4.1 Periodic driving systems -- 8.4.2 Pullback attractors with singleton component sets -- 8.4.3 Distal dynamical systems -- Pullback attractors of C-analytic systems -- 9.1 C-analytic cocycles -- 9.2 Some general facts about non-autonomous dynamical systems -- 9.3 Positively uniformly stable cocycles -- 9.4 The compact global pullback attractors of C-analytic cocycles with 9.4 The compact global pullback attractors of C-analytic cocycles with -- 9.5 The uniform dissipative cocycles with noncompact base -- 9.6 The compact and local dissipative cocycles with noncompact base -- 9.7 Applications -- 9.7.1 ODEs -- 9.7.2 Caratheodory di erential equations -- 9.7.3 ODEs with impulses -- Pullback attractors under discretization -- 10.1 Non-autonomous dynamical systems and pullback attractors -- 10.2 Non-autonomous quasi-linear di erential equation -- 10.3 Cocycle property -- 10.4 Main result -- 10.4.1 Existence of an absorbing set -- 10.4.2 Upper semi-continuity of the pullback attractor component sets -- 10.4.3 Upper semi-continuous convergence of the discretized pullback attractors -- 10.4.4 Upper semi-continuous convergence of the discretized global attractors -- 10.5 Singleton set-valued pullback attractor case -- 10.6 Appendix: Proof of Lemma 10.4 -- Global attractors of non-autonomous Global attractors of non-autonomous -- 11.1 Non-autonomous Navier-Stokes equations -- 11.2 Attractors of non-autonomous dynamical systems -- 11.3 Almost periodic and recurrent solutions of non-autonomous Navier-Stokes equations -- 11.4 Uniform averaging for a -- 11.5 The global averaging principle for Navier-Stokes equations -- Global attractors of V -monotone dynamical systems -- 12.1 Global attractors of V -monotone NDS -- 12.2 On the structure of Levinson center of V -monotone NDS -- 12.3 Almost periodic solutions of V -monotone systems.

12.4 Pullback attractors of V -monotone NDS -- 12.5 Applications -- 12.5.1 Finite-dimensional systems -- 12.5.2 Caratheodory's di erential equations -- 12.5.3 ODEs with impulse -- 12.5.4 Evolution equations with monotone operators -- Linear almost periodic dynamical systems -- 13.1 Bounded motions of linear systems -- 13.2 Bounded solutions of linear equations -- 13.3 Finite-dimensional systems -- 13.4 Relationship between di erent types of stability -- 13.5 Linear alpha-condensing systems -- 13.6 Exponential stable systems -- 13.7 Linear system with a minimal base -- 13.8 Some classes of uniformly exponentially stable equations -- 13.9 Linear periodic systems -- 13.9.1 Exponential stable linear periodic dynamical systems -- 13.9.2 Some classes of linear uniformly exponentially stable periodic di -- Triangular maps -- 14.1 Triangular maps and non-autonomous dynamical systems -- 14.2 Linear non-autonomous dynamical systems -- 14.3 Quasi-linear non-autonomous dynamical systems -- 14.4 Global attractors of quasi-linear triangular systems -- 14.5 Almost periodic and recurrent solutions -- 14.6 Pseudo recurrent solutions -- 14.7 Chaos in triangular maps -- Bibliography -- Index.