Author | Dymnikov, Valentin P. author |
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Title | Mathematics of Climate Modeling [electronic resource] / by Valentin P. Dymnikov, Aleksander N. Filatov |
Imprint | Boston, MA : Birkhรคuser Boston, 1997 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4148-5 |
Descript | XVI, 264 p. online resource |
1. Dynamical Systems. Attractors, Invariant Measures -- 1.1 Metric Spaces. Compactness -- 1.2 Dynamical Systems. Main Properties -- 1.3 Invariant Sets -- 1.4 Classification of Motions -- 1.5 Recurrence of Domains -- 1.6 Measure. Krylov-Bogolyubov Theorem -- 1.7 Dynamical Systems with Invariant Measure -- 1.8 Nonlinear Dissipative Systems -- 1.9 Inertial Manifolds of Dissipative Systems -- 2. Non-Autonomous Dissipative Systems, their Attractor and Averaging -- 2.1 Introduction -- 2.2 Processes and their Attractors. Kernel of Processes, Section of Kernel -- 2.3 Families of Processes and their Attractors -- 2.4 Family of Processes and Semigroups -- 2.5 Averaging of Nonlinear Dissipative Systems. Closeness between Attractors of Original and Averaged Systems -- 2.6 On Closeness of Solutions of Original and Averaged Nonlinear Dissipative Systems on Infinite Time Interval -- 3. Analysis of Barotropic Model -- 3.1. Existence of Global Attractor -- 3.2 Estimate of Dimension of Attractor -- 3.3 Statistical Solutions and Invariant Measures on Attractor -- 3.4 Estimate of Attractor Dimension with Respect to Orography -- 3.5 Galerkin Approximations -- 3.6 Existence of Inertial Manifold -- 4. Discretization of Systems Possessing Attractor -- 4.1 Discretization of Systems Possessing Inertial Manifolds -- 4.2 Time-Space Discretization of Systems Possessing Attractor -- 4.3 Globally Stable Difference Schemes for Barotropic Vorticity Equation -- 5. Numerical Study of Structure of Attractor Generated by Barotropic Equations on Sphere -- 5.1 Equations and Parameters of Model. Methods of Solving of Stationary and Nonstationary Problems -- 5.2 Statistical Stationary Solution and Stationary Points -- 5.3 Lyapunov Exponents and Attractor Dimension -- 5.4 Analysis of Analytical Estimates of Attractor Dimension of Barotropic Atmospheric Equations -- 6. Two-Layer Baroclinic Model -- 6.1 Two-Layer Baroclinic Model -- 6.2 Estimate of Attractor Dimension -- 6.3 Numerical Investigation of Attractor. Characteristics of Two-Layer Baroclinic Model -- 7. Investigation of Structure of Climate Attractors by Observed Data Series -- 7.1. Correlation Dimension of Attractor -- 7.2. Calculation of Lyapunov Exponents -- 7.3 Statistically Independent Degrees of Freedom and Attractor Dimension -- 8. Regimes of Atmosphere Circulation -- 8.1 Definition of Atmosphere Circulation Regimes -- 8.2 Dynamical Theory of Two-Regime Barotropic Circulation -- 8.3. Statistical Theory of Two-Regime Barotropic Circulation -- 8.4 S-Regimes of Atmosphere Circulation -- 9. Solvability of Ocean and Atmosphere Models -- 9.1 Introduction -- 9.2 Solvability of Ocean and Atmosphere Models in Bounded Domains -- 9.3 Solvability of Ocean and Atmosphere Models on Sphere in p-System of Coordinates