Quotient Manifold Projections and Hierarchical Dynamics

Details Quotient Manifold Projections and Hierarchical Dynamics Quotient Manifold Projections and Hierarchical Dynamics

2006-06-04

arxiv.org/abs/math-ph/0606016v1

Physics

Mathematical Physics

Scientific paper

In this paper we explore the mathematical structure of hierarchical organization in smooth dynamical systems. We start by making precise what we mean by a level in a hierarchy, and how the higher le vels need to respect the dynamics on the lower levels. We derive a mathematical construction for identifying distinct levels in a hierarchical dynamics. The construction is expressed through a quotient manifold of the phase space and a Lie group that fulfills certain requirement with respect to the flow. We show that projections up to higher levels can be related to symmetries of the dynamical system. We also discuss how the quotient manifold projections relate to invariant manifolds, invariants of the motion, and Noether's theorem.

Affiliated with

Also associated with

No associations

Rating

Quotient Manifold Projections and Hierarchical Dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quotient Manifold Projections and Hierarchical Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quotient Manifold Projections and Hierarchical Dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-98097