Analysis/Dynamical Systems Seminar
نویسنده
چکیده
In this talk, we will describe a dynamical mechanism called transverse ho-moclinic intersection. On one hand, the discovery of this mechanism proved to be very costly for a great mathematician. On the other hand, this mechanism provides the key idea to design very low energy paths that have been used to save millions of dollars for international spaceflight programs. We prove that, generically, every hyperbolic closed geodesic on a convex sphere admits transverse homoclinic intersections.
منابع مشابه
The Study of Nonlinear Dynamical Systems Nuclear Fission Using Hurwitz Criterion
In this paper, the nonlinear dynamic system of equations, a type of nuclear ssion reactor is solved analytically and numerically. Considering that the direct solution of three-dimensional dynamical systems analysis and more in order to determine the stability and instability, in terms of algebraicsystems is dicult. Using certain situations in mathematics called Hurwitz criterion, Necessary and ...
متن کاملDynamical Behavior of a Rigid Body with One Fixed Point (Gyroscope). Basic Concepts and Results. Open Problems: a Review
The study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1) to outline the characteristic features of...
متن کاملApplication of Dynamical Systems in Cancer Therapy
In this paper, we have proposed and analyzed a mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations.
متن کاملFractional dynamical systems: A fresh view on the local qualitative theorems
The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...
متن کاملSynchronization criteria for T-S fuzzy singular complex dynamical networks with Markovian jumping parameters and mixed time-varying delays using pinning control
In this paper, we are discuss about the issue of synchronization for singular complex dynamical networks with Markovian jumping parameters and additive time-varying delays through pinning control by Takagi-Sugeno (T-S) fuzzy theory.The complex dynamical systems consist of m nodes and the systems switch from one mode to another, a Markovian chain with glorious transition probabili...
متن کامل