Computability of Limit Sets for Two-Dimensional Flows

A classical theorem of Peixoto qualitatively characterizes, on the two-dimensional unit ball, the limit sets of structurally stable flows defined by ordinary differential equations. Peixoto’s density theorem further shows that such flows are typical in the sense that structurally stable systems form...

Full description

Saved in:
Bibliographic Details
Published inConnecting with Computability Vol. 12813; pp. 494 - 503
Main Authors Graça, Daniel S., Zhong, Ning
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2021
Springer International Publishing
SeriesLecture Notes in Computer Science
Online AccessGet full text

Cover

More Information
Summary:A classical theorem of Peixoto qualitatively characterizes, on the two-dimensional unit ball, the limit sets of structurally stable flows defined by ordinary differential equations. Peixoto’s density theorem further shows that such flows are typical in the sense that structurally stable systems form an open dense set in the space of all continuously differentiable flows. In this note, we discuss the problem of explicitly finding the limit sets of structurally stable planar flows.
ISBN:3030800482
9783030800482
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-80049-9_48