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 Guo, Boling, author.
 Berlin : Walter de Gruyter GmbH., [2018]
 Description
 Book — 1 online resource.
 Han, Xiaoying (Mathematician)
 Cham : Springer, c2017.
 Description
 Book — 1 online resource.
 Summary

 Part I Dynamical systems and numerical schemes. 1 Lyapunov stability and dynamical systems. 2 One step numerical schemes. Part II Steady states under discretization. 3 Linear systems. 4 Lyapunov functions. 5 Dissipative systems with steady states. 6 Saddle points under discretisation . Part III Autonomous attractors under discretization. 7 Dissipative systems with attractors. 8 Lyapunov functions for attractors. 9 Discretisation of an attractor. Part IV Nonautonomous limit sets under discretization. 10 Dissipative nonautonomous systems . 11 Discretisation of nonautonomous limit sets. 12 Variable step size. 13 Discretisation of a uniform pullback attractor. Notes. References.
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 Balint, Ștefan, Dr.
 Cambridge, UK : Cambridge Scientific Publishers, c2008.
 Description
 Book — 206 p. : ill. ; 25 cm.
 Online
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QA614.813 .B35 2008  Available 
 Buescu, Jorge, 1964
 Basel ; Boston : Birkhäuser Verlag, c1997.
 Description
 Book — xiii, 130 p. : ill. (some col.) ; 24 cm.
 Summary

This work on attractors in dynamical systems is intended primarily for researchers and advanced postgraduate students working in the area of dynamical systems. However, since it is selfcontained, it may be used by anyone wishing a general but mathematically rigorous introduction to the concepts and ideas of attractors in dynamics. The study is divided roughly into two: a generic introduction to the concept of attractors in dynamics, followed by a description of results on two research problems.
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QA614.813 .B84 1997  Available 
 Guo, Boling, author.
 Berlin ; Boston : De Gruyter, [2018]
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 Frontmatter
 Preface
 Contents
 1. Discrete attractor and approximate calculation
 2. Some properties of global attractor
 3. Structures of small dissipative dynamical systems
 4. Existence and stability of solitary waves
 Bibliography
 Index
 Cholewa, Jan W.
 Cambridge, UK ; New York : Cambridge University Press, 2000.
 Description
 Book — xii, 235 p. ; 23 cm.
 Summary

 Preface
 1. Preliminary concepts
 2. The abstract Cauchy problem
 3. Semigroups of global solutions
 4. Construction of the global attractor
 5. Application of abstract results to parabolic equations
 6. Examples of global attractors in parabolic problems
 7. Backward uniqueness and regularity of solutions
 8. Extensions
 9. Appendix Bibliography Index.
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QA614.813 .C48 2000  Available 
 LaniWayda, Bernhard, 1961
 Providence, R.I. : American Mathematical Society, 2001.
 Description
 Book — ix, 121 p. : ill. ; 26 cm.
 Summary

 Introduction Symbolic dynamics for maps Composition of 'local' and 'global' maps Linking equations and maps Explicit examples Appendix (Auxiliary results) References Figures.
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Shelved by Series title NO.718  Unknown 
 Kloeden, Peter E., author.
 New Jersey : World Scientific, [2021]
 Description
 Book — 1 online resource
 Summary

 Autonomous dynamical systems
 Nonautonomous dynamical systems: processes
 Skew product flows
 Entire solutions and invariant sets
 Attractors
 Nonautonomous equilibrium solutions
 Attractors for processes
 Examples of pullback attractors for processes
 Attractors of skew product flows
 Limitations of pullback attractors of processes
 Forward attractors
 Omegalimit sets and forward attracting sets
 Random dynamical systems
 Meansquare random dynamical systems
 Zelik, Sergey, 1972
 Providence, R.I. : American Mathematical Society, 2009.
 Description
 Book — vi, 97 p. ; 26 cm.
 Summary

The authors study semi linear parabolic systems on the full space Rn that admit a family of exponentially decaying pulselike steady states obtained via translations. The multipulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global centermanifold reduction theorem for the temporal evolution of such multipulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai  Bunimovich spacetime chaos in ID spacetime periodically forced Swift  Hohenberg equation.
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Shelved by Series title NO.925  Unknown 
 Gilmore, Robert, 1941
 New York : Wiley, c2002.
 Description
 Book — xxiii, 495 p. : ill. ; 25 cm.
 Summary

 Preface.
 1. Introduction.
 2. Dscrete Dynamical Systems: Maps.
 3. Continuous Dynamical Systems: Flows.
 4. Topological Invariants.
 5. Branched Manifolds.
 6. Topological Analysis Program.
 7. Folding Mechanisms: A2.
 8. Tearing Mechanisms: A3.
 9. Unfoldings.
 10. Symmetry.
 11. Flows in Higher Dimensions.
 12. Program for Dynamical Systems Theory. Appendix A: Determining Templates from Topological Invariants. References. Topic Index.
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QA614.813 .G55 2002  Unknown 
 Hunt, Fern Y.
 Gaithersburg, MD : U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, [1998]
 Description
 Book — 16 p.
 Online
Green Library
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Find it Bing Wing lower level: Microform cabinets  
C 13.58:6182  Inlibrary use 
 Chepyzhov, Vladimir V., 1962
 Providence, R.I. : American Mathematical Society, c2002.
 Description
 Book — xi, 363 p. ; 27 cm.
 Summary

 Introduction Attractors of autonomous equations: Attractors of autonomous ordinary differential equations Attractors of autonomous partial differential equations Dimension of attractors Attractors of nonautonomous equations: Processes and attractors Translation compact functions Attractors of nonautonomous partial differential equations Semiprocesses and attractors Kernels of processes Kolmogorov $\varepsilon$entropy of attractors Trajectory attractors: Trajectory attractors of autonomous ordinary differential equations Attractors in Hausdorff spaces Trajectory attractors of autonomous equations Trajectory attractors of autonomous partial differential equations Trajectory attractors of nonautonomous equations Trajectory attractors of nonautonomous partial differential equations Approximation of trajectory attractors Perturbation of trajectory attractors Averaging of attractors of evolution equations with rapidly oscillating terms Proofs of Theorems II.1.4 and II.1.5 Lattices and coverings Bibliography Index.
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QA1 .A5225 V.49  Unknown 
 Cheban, David N.
 2nd ed.  Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2015.
 Description
 Book — xxv, 589 p.
 Summary

 Global Attractors of Autonomous and NonAutonomous Dynamical Systems The Structure of Levinson Center of Dynamical System Holomorphic Dynamical Systems and Their Attractors Method of Lyapunov Functions Upper Semicontinuity of Attractors The Relationship Between Pullback, Forward and Global Attractors Pullback Attractors Under Discretization Global Attractors of Some Classes of Evolution Equations (Lorenz Systems, NavierStokes Equations, VMonotone Systems, Difference Equations etc.) Linear Almost Periodic Systems Global Attractors and Asymptotic Stability of Control Systems.
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 Lu, Kening, 1962
 Providence, Rhode Island : American Mathematical Society, 2013.
 Description
 Book — v, 85 pages : illustrations ; 25 cm.
 Summary

 Introduction Basic Definitions and Facts Statement of Theorems Invariant Manifolds Canonical Form of Equations Around the Limit Cycle Preliminary Estimates on Solutions of the Unforced Equation Time$T$ Map of Forced Equation and Derived $2$D System Strange Attractors with SRB Measures Application: The Brusselator Appendix A. Proofs of Propositions 3.13.3 Appendix B. Proof of Proposition 7.5 Appendix C. Proofs of Proposition 8.1 and Lemma 8.2 Bibliography.
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Shelved by Series title NO.1054  Unknown 
15. Dimensions, embeddings, and attractors [2011]
 Robinson, James C. (James Cooper), 1969
 Cambridge, UK ; New York : Cambridge University Press, 2011.
 Description
 Book — xii, 205 p. : ill. ; 24 cm.
 Summary

 Preface Introduction Part I. FiniteDimensional Sets:
 1. Lebesgue covering dimension
 2. Hausdorff measure and Hausdorff dimension
 3. Boxcounting dimension
 4. An embedding theorem for subsets of RN
 5. Prevalence, probe spaces, and a crucial inequality
 6. Embedding sets with dH(XX) finite
 7. Thickness exponents
 8. Embedding sets of finite boxcounting dimension
 9. Assouad dimension Part II. FiniteDimensional Attractors:
 10. Partial differential equations and nonlinear semigroups
 11. Attracting sets in infinitedimensional systems
 12. Bounding the boxcounting dimension of attractors
 13. Thickness exponents of attractors
 14. The Takens timedelay embedding theorem
 15. Parametrisation of attractors via point values Solutions to exercises References Index.
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QA611.3 .R63 2011  Unknown 
 Jäger, Tobias H., 1976
 Providence, R.I. : American Mathematical Society, 2009.
 Description
 Book — vi, 106 p. : ill. ; 26 cm.
 Summary

The author proposes a general mechanism by which strange nonchaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddlenode bifurcation, but instead of a neutral invariant curve there exists a strange nonchaotic attractorrepeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls 'exponential evolution of peaks'.
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Shelved by Series title NO.945  Unknown 
 Cheban, David N.
 Singapore ; Hackensack, N.J. : World Scientific, c2004.
 Description
 Book — xxiii, 502 p.
 Summary

 Autonomous Dynamical Systems NonAutonomous Dissipative Dynamical Systems Analytic Dissipative Systems The Structure of the Levinson Centre of System with the Condition of the Hyperbolicity Method of Lyapunov Functions Dissipativity of Some Classes of Equations Upper SemiContinuity of Attractors The Relationship between Pullback, Forward and Global Attractors Pullback Attractors of Analytic Systems Pullback Attractors Under Discretization Global Attractors of NonAutonomous NavierStokes Equations Global Attractors of VMonotone Dynamical Systems Linear Almost Periodic Dynamical Systems Triangular Maps.
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 Ladyzhenskaya, Olga.
 Cambridge : Cambridge University Press, 1991.
 Description
 Book — 1 online resource (88 p.) : digital, PDF file(s).
 Summary

 Preface Part I: Attractors for the semigroups of operators
 1. Basic notions
 2. Semigroups of class K
 3. Semigroups of class AK
 4. On dimensions of compact invariant sets Part II: Semigroups generated by evolution equations
 5. Introduction to Part II
 6. Estimates for the number of determining modes and the fractal dimension of bounded invariant sets for the NavierStokes equations
 7. Evolution equations of hyperbolic type References Index.
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19. Attraction in numerical minimization : iteration mappings, attractors, and basins of attraction [2018]
 Levy, Adam B.
 Cham, Switzerland : Springer, 2018.
 Description
 Book — 1 online resource Digital: text file.PDF.
 Summary

 Multisets and multiset mappings
 Iteration mappings
 Equilibria in dynamical systems
 Attractors
 Basin analysis via simulation.
 Chueshov, Igor, 1951
 Providence, R.I. : American Mathematical Society, c2008.
 Description
 Book — viii, 183 p. ; 26 cm.
 Summary

 Introduction Abstract results on global attractors Existence of compact global attractors for evolutions of the second order in time Properties of global attractors for evolutions of the second order in time Semilinear wave equation with a nonlinear dissipation Von Karman evolutions with a nonlinear dissipation Other models from continuum mechanics Bibliography Index.
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Shelved by Series title NO.912  Unknown 
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