The Periodicity Theorem , Talk 1 Vitaly

The Periodicity Theorem, Talk 2

Periodicity in a System of Differential Equations with Finite Delay

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

Bott periodicity

1 Description The Periodicity Theorem was proved by Raoul Bott over fifty years ago (cf. survey [3], [4], [9]) and quickly became one of the strongest tools in homotopy theory, topology of manifolds and global analysis. The original theorem asserted that homotopy groups of the linear groups GL(n,F) where F is the field of real, complex or quaternion numbers are periodic i.e. πi(GL(k,F) ' πi+nF(...

اثر تناوب بهره‌برداری سقز بر زادآوری طبیعی درختان بنه (مطالعه موردی: جنگل‌های بنه استان کردستان، سنندج)

In order to evaluate the impacts of oleo-gum resin extraction periodicity on natural regeneration of wild pistachio (Pistacia atlantica subsp. kurdica), three different forest areas in Kurdistan province, west of Iran, were selected based on difference extraction periodicities (regular periodicity, irregular periodicity and without periodicity). Then homogenous unit maps in GIS produced, and on...

The Bott Periodicity Theorem

The Bott periodicity theorem is of fundamental importance in many areas of mathematics, from algebraic topology to functional analysis. It appears unexpectedly in different guises and I would like to explain some of these as well as the influence it has had on the development of different fields. I will concentrate on two roles that periodicity plays. First, periodicity allows one to deloop cla...