Almost periodicity, chaos, and asymptotic equivalence

The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology.Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients;Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area;Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity;Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.


Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients
Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005)
In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...
Dosi, A. (American Mathematical Society (AMS), 2020-01-01)
The paper is devoted to a noncommutative holomorphic functional calculus and its application to noncommutative algebraic geometry. A description is given for the noncommutative (infinite-dimensional) affine spaces A(q)(x), 1 = 0, are calculated.
Convergence performance of the approximate factorization methods with multi-block implicit boundary conditions at hypersonic speeds
Koca, Melikşah; Eyi, Sinan; Department of Aerospace Engineering (2022-9)
This thesis study presents convergence characteristics of the implicit approximate factorization methods at hypersonic flow conditions and with 2-dimensional and 3-dimensional geometries. The efficiency of the implicit boundary conditions at block interfaces for the multi-block grids is investigated for different approximate factorization methods. Standard Alternating Direction Implicit (ADI) method, Diagonal Dominant Alternating Direction Implicit method (DDADI) with and without Huang’s sub-iteration corre...
Regularity and stochasticity of nonlinear dynamical systems
Akhmet, Marat (Springer, 2017-06-01)
This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing ...
Finite Volume Method For Hyperbolic Conservation Laws On Manifolds
Okutmuştur, Baver (LAP LAMBERT Academic Publishing, 2017-03-01)
The purpose of this book is to lay out a mathematical framework for the convergence and error analysis of the finite volume method for the discretization of hyperbolic conservation laws on manifolds. Finite Volume Method (FVM) is a discretization approach for the numerical simulation of a wide variety physical processes described by conservation law systems. It is extensively employed in fluid mechanics, meteorology, heat and mass transfer, electromagnetic, models of biological processes and m...
Citation Formats
M. Akhmet, Almost periodicity, chaos, and asymptotic equivalence. 2019.