Subexponential instability in one-dimensional maps implies infinite invariant measure

Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basis

We consider a generalisation of Ulam’s method for approximating invariant densities of one-dimensional maps. Rather than use piecewise constant polynomials to approximate the density, we use polynomials of degree n which are defined by the requirement that they preserve the measure on n+1 neighbouring subintervals. Over the whole interval, this results in a discontinuous piecewise polynomial ap...

Translationally invariant discrete kinks from one-dimensional maps.

For most discretizations of the phi4 theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional discretizations that allow stationary kinks to be centered anywhere between the sites. We show that this translational invariance of the kink implies the existence of an underlying one-dimensional map phi(n+1) =F (phi(n)) ...

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

Invariant measure for an infinite neural network

Smooth Invariant Foliations in Infinite Dimensional Spaces

One of the most useful properties of dynamical systems is the existence of invariant manifolds and their invariant foliations near an equilibrium or a periodic orbit. These manifolds and foliations serve as a convenient setting to describe the qualitative behavior of the local flows, and in many cases they are useful tools for technical estimates which facilitate the study of the local bifurcat...