Dynamics with Chaos and Fractals

Stands as the first book presenting theoretical background on the unpredictable point and mapping of fractals.Introduces the concepts of unpredictable functions, abstract self-similarity, and similarity map.Discusses unpredictable solutions of quasilinear ordinary and functional differential equations.Illustrates new ways to construct fractals based on the ideas of Fatou and Julia. Examines unpredictability in ocean dynamics and neural networks, chaos in hybrid systems on a time scale, and homoclinic and heteroclinic motions in economic models.


Dynamics for chaos and fractals
Alejaily, Ejaily; Akhmet, Marat; Department of Mathematics (2019)
In this thesis, we study how to construct and analyze dynamics for chaos and fractals. After the introductory chapter, we discuss in the second chapter the chaotic behavior of hydrosphere parameters and their influence on global weather and climate. For this purpose, we investigate the nature and source of unpredictability in the dynamics of sea surface temperature. The impact of sea surface temperature variability on the global climate is clear during some global climate patterns like the El Niño-Southern ...
Algebraic curves hermitian lattices and hypergeometric functions
Zeytin, Ayberk; Önsiper, Mustafa Hurşit; Department of Mathematics (2011)
The aim of this work is to study the interaction between two classical objects of mathematics: the modular group, and the absolute Galois group. The latter acts on the category of finite index subgroups of the modular group. However, it is a task out of reach do understand this action in this generality. We propose a lattice which parametrizes a certain system of ”geometric” elements in this category. This system is setwise invariant under the Galois action, and there is a hope that one can explicitly under...
Hybrid wavelet-neural network models for time series data
Kılıç, Deniz Kenan; Uğur, Ömür; Department of Financial Mathematics (2021-3-3)
The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps better modeling in the sense of both frequency and time. S&P500 (∧GSPC) and NASDAQ (∧ IXIC) data are divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. ...
Learning by optimization in random neural networks
Atalay, Mehmet Volkan (1998-10-28)
The random neural network model proposed by Gelenbe has a number of interesting features in addition to a well established theory. Gelenbe has also developed a learning algorithm for the recurrent random network model using gradient descent of a quadratic error function. We present a quadratic optimization approach for learning in the random neural network, particularly for image texture reconstruction.
Monte Carlo analysis of ridged waveguides with transformation media
Ozgun, Ozlem; Kuzuoğlu, Mustafa (Wiley, 2013-07-01)
A computational model is presented for Monte Carlo simulation of waveguides with ridges, by combining the principles of transformation electromagnetics and the finite methods (such as finite element or finite difference methods). The principle idea is to place a transformation medium around the ridge structure, so that a single and easy-to-generate mesh can be used for each realization of the Monte Carlo simulation. Hence, this approach leads to less computational resources. The technique is validated by me...
Citation Formats
M. Akhmet, Dynamics with Chaos and Fractals. 2020.