Ergodic Theory

Ergodic theory deals with the study of invariant measures in dynamical systems. "Measures" are generalizations of concepts such as length, area, volume, etc. "Invariant measures" are measures that are preserved by functions. "Dynamical systems" are systems in which a fixed rule governs the time dependence of points in a geometric space, such as the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish in a lake each spring.

An introductory class in ergodic theory is likely to include the following topics:

• Measure-preserving transformations
• Isomorphism, conjugacy, and spectral isomorphism
• Measure-preserving transformations with discrete spectrum
• Entropy
• Topological dynamics
• Invariant measures for continuous transformations
• Topological entropy
• Relationship between topological entropy and measure-theoretic entropy
• Topological pressure and its relationship with invariant measures

There is no lack of books on this interesting mathematical topic, some of which can be seen on Amazon.com or Google. In addition, students should spend time with the journal of Ergodic Theory and Dynamical Systems, put out by Cambridge Journals Online.

To fulfill our tutoring mission of online education, our college homework help and online tutoring centers are standing by 24/7, ready to assist college students who need homework help with all aspects of ergodic theory. Our mathematics tutors can help with all your projects, large or small, and we challenge you to find better online ergodic theory tutoring anywhere.