Immersion in Complex Dynamical Systems with Ergodicity

Authors

  • Rômulo Damasclin Chaves dos Santos Department of Physics, Technological Institute of Aeronautics, São Paulo, Brazil https://orcid.org/0000-0002-9482-1998
  • Jorge Henrique de Oliveira Sales State University of Santa Cruz – Department of Exact Sciences, Ilhéus, Bahia, Brazil https://orcid.org/0000-0003-1992-3748

DOI:

https://doi.org/10.18540/jcecvl10iss5pp18642

Keywords:

Entropy., Topological Pressure., Ergodicity., Turbulence in Fluids., Complex Dynamic Systems.

Abstract

This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion progresses to explore discrete topological entropy and its significance within dynamical systems, culminating in the introduction of topological entropy pressure as a nuanced form of this concept. The study then investigates various applications of topological entropy within dynamic systems, emphasizing its utility in understanding chaotic systems and its role in ergodic theory. A novel theory, termed Topological Ergodic Entropy Theory (TEET), is presented, offering a fresh perspective on the analysis of ergodic dynamical systems. Furthermore, the work introduces the Ergodic Theory of Turbulent Flow (ETTF), which probes the interplay between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. Through these explorations, the findings contribute significantly to the comprehension of the intricate nature of dynamical systems and their diverse applications across mathematics and physics. By scrutinizing topological entropy and its implications in dynamical systems, this research offers novel insights into the chaotic and stochastic behaviors exhibited by these systems. Additionally, the introduction of pioneering theories like ETTF opens up new avenues for understanding and modeling turbulent phenomena, thereby enriching our understanding of complex dynamical processes.

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Published

2024-04-14

How to Cite

Santos, R. D. C. dos, & Sales, J. H. de O. (2024). Immersion in Complex Dynamical Systems with Ergodicity. The Journal of Engineering and Exact Sciences, 10(5), 18642. https://doi.org/10.18540/jcecvl10iss5pp18642

Issue

Section

General Articles