On the Poincaré index of isolated invariant sets

M. R. Razvan; M. Fotouhi

On the Poincaré index of isolated invariant sets

M. R. Razvan
, M. Fotouhi^*

^*Corresponding author for this work

Research output: Journal Publication › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, the Conley index theory is used to examine the Poincaré index of an isolated invariant set. Some limiting conditions on a critical point of a planar vector field are obtained to be an isolated invariant set. As a result, the existence of infinitely many homoclinic orbits for a critical point with the Poincaré index greater than one is shown.

Original language	English
Pages (from-to)	574-577
Number of pages	4
Journal	Scientia Iranica
Volume	15
Issue number	6
Publication status	Published - 2008
Externally published	Yes

Free Keywords

Conley index
Homoclinic orbit
Poincaré-Lefchetz duality
Poincré index

ASJC Scopus subject areas

General Engineering

Cite this

@article{01e643ecc500412d8cd33106e615956b,

title = "On the Poincar{\'e} index of isolated invariant sets",

abstract = "In this paper, the Conley index theory is used to examine the Poincar{\'e} index of an isolated invariant set. Some limiting conditions on a critical point of a planar vector field are obtained to be an isolated invariant set. As a result, the existence of infinitely many homoclinic orbits for a critical point with the Poincar{\'e} index greater than one is shown.",

keywords = "Conley index, Homoclinic orbit, Poincar{\'e}-Lefchetz duality, Poincr{\'e} index",

author = "Razvan, \{M. R.\} and M. Fotouhi",

year = "2008",

language = "English",

volume = "15",

pages = "574--577",

journal = "Scientia Iranica",

issn = "1026-3098",

publisher = "Sharif University of Technology",

number = "6",

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T1 - On the Poincaré index of isolated invariant sets

AU - Razvan, M. R.

AU - Fotouhi, M.

PY - 2008

Y1 - 2008

N2 - In this paper, the Conley index theory is used to examine the Poincaré index of an isolated invariant set. Some limiting conditions on a critical point of a planar vector field are obtained to be an isolated invariant set. As a result, the existence of infinitely many homoclinic orbits for a critical point with the Poincaré index greater than one is shown.

AB - In this paper, the Conley index theory is used to examine the Poincaré index of an isolated invariant set. Some limiting conditions on a critical point of a planar vector field are obtained to be an isolated invariant set. As a result, the existence of infinitely many homoclinic orbits for a critical point with the Poincaré index greater than one is shown.

KW - Conley index

KW - Homoclinic orbit

KW - Poincaré-Lefchetz duality

KW - Poincré index

UR - https://www.scopus.com/pages/publications/58649100060

M3 - Article

AN - SCOPUS:58649100060

SN - 1026-3098

VL - 15

SP - 574

EP - 577

JO - Scientia Iranica

JF - Scientia Iranica

IS - 6

ER -

On the Poincaré index of isolated invariant sets

Abstract

Free Keywords

ASJC Scopus subject areas

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