/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Recurrence plots for the analysis of complex systems

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

/pdf/introduction-to-the-modern-theory-of-dynamical-systems-1eced70mum.pdf

Introduction to the Modern Theory of Dynamical Systems

Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

For subshifts of finite type, conformal repellers, and conformal horseshoes, we prove that the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages do not exist simultaneously, carries full topological entropy and full Hausdorff dimension. This follows from a much stronger statement formulated for a class of symbolic dynamical systems which includes subshifts with the specification property. Our proofs strongly rely on the multifractal analysis of dynamical systems and constitute a non-trivial mathematical application of this theory.

Sets of "non-typical" points have full topological entropy and full hausdorff dimension

Introduction Lyapunov stability theory of differential equations Elements of nonuniform hyperbolic theory Examples of nonuniformly hyperbolic systems Local manifold theory Ergodic properties of smooth hyperbolc measures Bibliography Index

Lyapunov Exponents and Smooth Ergodic Theory

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

Luis Barreira

Papers

Sets of "non-typical" points have full topological entropy and full hausdorff dimension

Lyapunov Exponents and Smooth Ergodic Theory

Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents

Nonuniform Hyperbolicity: Ergodic Theory of Smooth and SRB Measures

Nonuniform Hyperbolicity: General Hyperbolic Measures