Reverse-engineering invariant manifolds with asymptotic phase

نویسندگان

  • Matthew Kvalheim
  • Shai Revzen
چکیده

2 Motivation: decomposition of NHIM-defining vector fields 3 2.1 The structure of the basin of attraction of a NHIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Persistence of this structure under perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Implications of NHIM results for model reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Statistical cosymplectic manifolds and their submanifolds

    In ‎this ‎paper‎, we introduce statistical cosymplectic manifolds and investigate some properties of their tensors. We define invariant and anti-invariant submanifolds and study invariant submanifolds with normal and tangent structure vector fields. We prove that an invariant submanifold of a statistical cosymplectic manifold with tangent structure vector field is a cosymplectic and minimal...

متن کامل

Epsilon-free Curvature Methods for Slow-fast Dynamical Systems

1. Introduction. Many dynamical systems exhibit a slow-fast structure where a solution from some arbitrary initial condition rapidly relaxes toward some attracting invariant manifold where the dynamics progresses slowly. Determining such manifolds is of obvious importance. On one hand they provide a basic insight into the dynamics of the system, on the other hand they allow a reduction of dimen...

متن کامل

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

متن کامل

Nonautonomous Discrete Dynamics: Discretization and Taylor Approximation

In this talk, we consider a class of nonautonomous difference equations (recursions) possessing an attractive invariant manifold in the extended state space. It is our aim to study the behavior of this manifold, as well as of its corresponding asymptotic phase under perturbation. Our framework is sufficiently general to include discrete counterparts of (center-)unstable and inertial manifolds. ...

متن کامل

Topological aspects of chaotic scattering in higher dimensions.

We investigate the topological properties of the chaotic invariant set associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the separation of one degree of freedom from the rest in the asymptotic regime, a common property in a large class of scattering models, defines a gate which is a dynamical object with phase space separating invariant manif...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016