Iterative roots of multidimensional operators and applications to dynamical systems

作者：Georgiev Pando^*; Kindermann Lars; Pardalos Panos M

来源：Optimization Letters, 2013, 7(8): 1701-1710.

DOI：10.1007/s11590-012-0532-2

• Iterative root
• Monotone operator
• Functional equation
• Dynamical system

Solutions phi(x) of the functional equation phi(phi(x)) = f (x) are called iterative roots of the given function f (x). They are of interest in dynamical systems, chaos and complexity theory and also in the modeling of certain industrial and financial processes. The problem of computing this "square root" of a function or operator remains a hard task. While the theory of functional equations provides some insight for real and complex valued functions, iterative roots of nonlinear mappings from to are less studied from a theoretical and computational point of view. Here we prove existence of iterative roots of a certain class of monotone mappings in spaces and demonstrate how a method based on neural networks can find solutions to some examples that arise from simple physical dynamical systems.

• 出版日期2013-12