A note on the convergence of parametrised non-resonant invariant manifolds

Tomas Johnson; Warwick Tucker

doi:10.1007/s12346-011-0040-2

A note on the convergence of parametrised non-resonant invariant manifolds

Tomas Johnson, Warwick Tucker

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

18 Citations (Scopus)

Abstract

Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds.

Original language	English
Pages (from-to)	107-121
Number of pages	15
Journal	Qualitative Theory of Dynamical Systems
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/s12346-011-0040-2
Publication status	Published - 1 Dec 2011
Externally published	Yes

Keywords

Auto-validated numerics
Hyperbolic fixed points
Invariant manifolds
Normal forms

Access to Document

10.1007/s12346-011-0040-2

Cite this

@article{9ba2eb72eb2a483ca15d7a411dee6efe,

title = "A note on the convergence of parametrised non-resonant invariant manifolds",

abstract = "Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds.",

keywords = "Auto-validated numerics, Hyperbolic fixed points, Invariant manifolds, Normal forms",

author = "Tomas Johnson and Warwick Tucker",

year = "2011",

month = dec,

day = "1",

doi = "10.1007/s12346-011-0040-2",

language = "English",

volume = "10",

pages = "107--121",

journal = "Qualitative Theory of Dynamical Systems",

issn = "1575-5460",

publisher = "Birkhauser",

number = "1",

}

TY - JOUR

T1 - A note on the convergence of parametrised non-resonant invariant manifolds

AU - Johnson, Tomas

AU - Tucker, Warwick

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds.

AB - Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds.

KW - Auto-validated numerics

KW - Hyperbolic fixed points

KW - Invariant manifolds

KW - Normal forms

UR - https://www.scopus.com/pages/publications/84896692987

U2 - 10.1007/s12346-011-0040-2

DO - 10.1007/s12346-011-0040-2

M3 - Article

AN - SCOPUS:84896692987

SN - 1575-5460

VL - 10

SP - 107

EP - 121

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

IS - 1

ER -

A note on the convergence of parametrised non-resonant invariant manifolds

Abstract

Keywords

Access to Document

Other files and links

Cite this