(A) In this paper we study some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Hausdorff) topological groups G on (Hausdorff) compact spaces X.

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Fraïssé Limits, Ramsey Theory, and topological dynamics of automorphism groups

The aim of this paper is to introduce and characterize observability and reconstructibility properties for Boolean networks and Boolean control networks, described according to the algebraic approach proposed by D. Cheng and co-authors in the series of papers [3], [6], [7] and in the recent monography . A complete characterization of these properties, based both on the Boolean matrices involved in the network description and on the corresponding digraphs, is provided. Finally, the problem of state observer design for reconstructible BNs and BCNs is addressed, and two different solutions are proposed.

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Observability, Reconstructibility and State Observers of Boolean Control Networks

We study in this paper some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures.

Fraisse Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups

Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior known as nonuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nonzero Lyapunov exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmuller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schrodinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields.

/pdf/nonuniform-hyperbolicity-dynamics-of-systems-with-nonzero-5dks9a0o5q.pdf

Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents

Pugh and Shub [PS3] have conjectured that essential accessibility implies ergodicity, for a C 2 , partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all partially hyperbolic systems with 1-dimensional center bundle. We also obtain ergodicity results for C 1+γ partially hyperbolic systems.

http://annals.math.princeton.edu/wp-content/uploads/annals-v171-n1-p09-p.pdf

On the ergodicity of partially hyperbolic systems

Introduction 1. Examples and basic concepts 2. Topological dynamics 3. Symbolic dynamics 4. Ergodic theory 5. Hyperbolic dynamics 6. Ergodicity of Anosov diffeomorphisms 7. Low-dimensional dynamics 8. Complex dynamics 9. Measure-theoretic entropy Bibliography Index.

http://catdir.loc.gov/catdir/samples/cam033/2002022281.pdf

Introduction to dynamical systems

The isometry group of a compact Lorentz manifold. II

A Guide to MATLAB®: Frontmatter

We show that a C0 minimal action of a semisimple Lie group without compact factors is either locally free or induced from a minimal action of a proper parabolic subgroup. We describe the orbit structure of the action restricted to a maximal compact subgroup, and then apply this to minimal actions in low dimension. We give some examples, applications, and open problems.

Minimal actions of semisimple groups

From the Publisher:
This is an easy-to-use text that uses Maple (a mathematical software system) to introduce symbolic, numerical, graphical, and qualitative techniques to differential equations. There is special emphasis on the specific features of Maple that are useful for analyzing differential equations and introduces mathematical issues pertinent to the use of numerical methods and computers such as stability, numerical error, and reliability.

Garrett Stuck

Papers

Introduction to dynamical systems

The isometry group of a compact Lorentz manifold. II

A Guide to MATLAB®: Frontmatter

Minimal actions of semisimple groups

Differential Equations with Maple