Simplicial dynamical systems / Ethan Akin.

Format:

Book

Author/Creator:

Akin, Ethan, 1946- author.

Series:

Memoirs of the American Mathematical Society ; no. 667.

Memoirs of the American Mathematical Society, 0065-9266 ; number 667

Language:

English

Subjects (All):

Topological dynamics.

Stability.

Differentiable dynamical systems.

Physical Description:

1 online resource (215 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1999]

Language Note:

English

Summary:

A simplicial dynamical system is a simplicial map $g: K DEGREES* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K DEGREES*$ is a proper subdivision of $K$, for example, the barycentric or any further subdivision. the dynamics of the asociated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continous map on $X$ can be $C DEGREES0$ approximated by such systems. Other examples yield interesting

Contents:

""Table of Contents""; ""Introduction""; ""1. Chain Recurrence and Basic Sets""; ""2. Simplicial Maps and Their Local Inverses""; ""3. The Shift Factor Maps for a Simplicial Dynamical System""; ""4. Recurrence and Basic Set Images""; ""5. Invariant Measures""; ""6. Generalized Simplicial Dynamical Systems""; ""7. Examples""; ""8. PL Roundoffs of a Continuous Map""; ""9. Nondegenerate Maps on Manifolds""; ""10. Appendix: Stellar and Lunar Subdivisions""; ""11. Appendix: Hyperbolicity for Relations""; ""References""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""

""J""""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""Z""

Notes:

"July 1999, volume 140, number 667 (first of 4 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0258-0