The Poincaré Manifold at A Stable Equilibrium of C2 Planar Flow

William Rivera; Richard Sowers

doi:10.1080/00036819408840236

The Poincaré Manifold at A Stable Equilibrium of C² Planar Flow

Research output: Contribution to journal › Article › peer-review

Abstract

We establish the existence of a unique C² local invariant manifold at the stable equilibrium of a C² vector field. Here, in contrast to the standard case, the eigenvalue ratio μ/λ is bounded above by the degree of smoothness of the vector field.

Original language	English (US)
Pages (from-to)	247-259
Number of pages	13
Journal	Applicable Analysis
Volume	52
Issue number	1-4
DOIs	https://doi.org/10.1080/00036819408840236
State	Published - Feb 1 1994
Externally published	Yes

Keywords

Poincaré manifold
Weak stable manifold
generalized center stable manifold
local invariant manifold
nonresonance inequality
strong stable manifold

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1080/00036819408840236

Library availability

Discover UIUC Full Text

Cite this

@article{907e37c15468458ca1be3c53016367a4,

title = "The Poincar{\'e} Manifold at A Stable Equilibrium of C2 Planar Flow",

abstract = "We establish the existence of a unique C2 local invariant manifold at the stable equilibrium of a C2 vector field. Here, in contrast to the standard case, the eigenvalue ratio μ/λ is bounded above by the degree of smoothness of the vector field.",

keywords = "Poincar{\'e} manifold, Weak stable manifold, generalized center stable manifold, local invariant manifold, nonresonance inequality, strong stable manifold",

author = "William Rivera and Richard Sowers",

year = "1994",

month = feb,

day = "1",

doi = "10.1080/00036819408840236",

language = "English (US)",

volume = "52",

pages = "247--259",

journal = "Applicable Analysis",

issn = "0003-6811",

publisher = "Taylor and Francis Ltd.",

number = "1-4",

}

TY - JOUR

T1 - The Poincaré Manifold at A Stable Equilibrium of C2 Planar Flow

AU - Rivera, William

AU - Sowers, Richard

PY - 1994/2/1

Y1 - 1994/2/1

N2 - We establish the existence of a unique C2 local invariant manifold at the stable equilibrium of a C2 vector field. Here, in contrast to the standard case, the eigenvalue ratio μ/λ is bounded above by the degree of smoothness of the vector field.

AB - We establish the existence of a unique C2 local invariant manifold at the stable equilibrium of a C2 vector field. Here, in contrast to the standard case, the eigenvalue ratio μ/λ is bounded above by the degree of smoothness of the vector field.

KW - Poincaré manifold

KW - Weak stable manifold

KW - generalized center stable manifold

KW - local invariant manifold

KW - nonresonance inequality

KW - strong stable manifold

UR - http://www.scopus.com/inward/record.url?scp=84948505676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948505676&partnerID=8YFLogxK

U2 - 10.1080/00036819408840236

DO - 10.1080/00036819408840236

M3 - Article

AN - SCOPUS:84948505676

SN - 0003-6811

VL - 52

SP - 247

EP - 259

JO - Applicable Analysis

JF - Applicable Analysis

IS - 1-4

ER -