Ergodic theory for smooth one dimensional dynamical systems

An introduction to Smooth Ergodic Theory for one-dimensional dynamical systems

SOME ERGODIC PROPERTIES OF HYPER MV {ALGEBRA DYNAMICAL SYSTEMS

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

Smooth Ergodic Theory

Conservative, Dissipative: Conservative dynamical systems (on a compact phase space) are those that preserve a finite measure equivalent to volume. Hamiltonian dynamical systems are important examples of conservative systems. Systems that are not conservative are called dissipative. Finding physically meaningful invariant measures for dissipative maps is a central object of study in smooth ergo...

Lyapunov Exponents and Smooth Ergodic Theory

This book provides a systematic introduction to smooth ergodic theory, including the general theory of Lyapunov exponents, nonuniform hyperbolic theory, stable manifold theory emphasizing absolute continuity of invariant foliations, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The book can be used as a primary textbook for a special topics course on nonuniform hy...

2011 Workshop on Nonlinear Analysis and Optimization Department of Mathematics National Taiwan Normal

Almost all of the technical methods, which are used in the theory of nonlinear dynamical systems, originated in the theory of one dimensional dynamical systems. In this talk, a relation between nonlinear ergodic theorems, which are developed by Prof. Takahashi and other researchers, and the asymptotic behavior of one dimensional dynamical systems will be delivered, and moreover, application of ...