Ultra Poincaré Chaos and Alpha Labeling

A new approach to chaotic dynamics

Author: Professor Marat Akhmet and Marat Akhmet Series: IOP ebooks

Hardcover

Ultra Poincaré chaos offers an alternative to Lorenz chaos, showcasing alpha unpredictability, which is a characteristic of an isolated motion. Alpha labeling is a valuable mathematical structure for studying complexity, as well as for the entirety of dynamical systems theory. Additionally, unique historical and philosophical insights enhance the understanding of the ongoing research.

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Summary

Description

This book serves as a comprehensive and detailed collection of knowledge on two innovative aspects of our research: ultra Poincaré chaos and alpha labeling. The first concept represents a fundamental trait of dynamical complexity, while the second acts as an algorithmic tool to analyse and construct complexity within the dynamics, probabilities, and geometries of science and industry.

The manuscript aims to provide solid guidance for studying complexities through rigorous mathematical methods. The chaos is derived from the dynamical characteristic of alpha unpredictability, representing a modernized version of Poisson stability motion. It builds upon the foundational work of Poincaré and Birkhoff, incorporating key new insights that expand upon the French genius’s contributions to the recurrence theorem, applicable in contexts such as the three-body problem.

Key Features:

Explores the complexities found in fractals, dynamical systems, and stochastic processes
Introduces an innovative analytical method for assessing random processes
Offers a fresh perspective on fractal geometries
Highlights the advantages of ultra Poincaré chaos
Includes historical and philosophical insights

About the Author

Dr. Marat Akhmet is presently a Professor in the Department of Mathematics at METU in Ankara, Turkey. In recent years, he has been exploring continuous and discontinuous dynamics, artificial neural networks alongside stability, chaos, and fractals. He has authored eight books and published over two hundred scientific papers.