Ultra Poincaré Chaos and Alpha Labeling

A new approach to chaotic dynamics

Professor Marat Akhmet (Middle East Technical University (Turkey))

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English

Institute of Physics Publishing
15 November 2024

Differential calculus & equations; Chaos theory; Mathematical physics

Series: IOP ebooks

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

By: Professor Marat Akhmet (Middle East Technical University (Turkey))
Imprint: Institute of Physics Publishing
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
ISBN: 9780750351607
ISBN 10: 0750351608
Series: IOP ebooks
Pages: 356
Publication Date: 15 November 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.