Unstable manifolds of a limit cycle near grazing

R Szalai; HM Osinga

Unstable manifolds of a limit cycle near grazing

Research output: Working paper › Working paper and Preprints

336 Downloads (Pure)

Abstract

We study the local dynamics of an impacting system near a grazing bifurcation point. In particular, we investigate local invariant manifolds of grazing periodic orbits. At a grazing bifurcation point the local return map does not have a Jacobian nor is of Lipschitz continuous, so that the classical theory does not apply. Nevertheless, we are able to use the Graph Transform technique and show that under certain conditions a local Lipschitz unstable manifold of the periodic orbit exists at the grazing bifurcation point.

Original language	English
Publication status	Published - 2007

Bibliographical note

Additional information: Submitted to the journal Nonlinearity

Keywords

global manifold
grazing bifurcation

Access to Document

PreprintSubmitted manuscript, 254 KB

http://hdl.handle.net/1983/917

Fingerprint Dive into the research topics of 'Unstable manifolds of a limit cycle near grazing'. Together they form a unique fingerprint.

Cite this

@techreport{3144d56a27984df4aad516aab7ba93b2,

title = "Unstable manifolds of a limit cycle near grazing",

abstract = "We study the local dynamics of an impacting system near a grazing bifurcation point. In particular, we investigate local invariant manifolds of grazing periodic orbits. At a grazing bifurcation point the local return map does not have a Jacobian nor is of Lipschitz continuous, so that the classical theory does not apply. Nevertheless, we are able to use the Graph Transform technique and show that under certain conditions a local Lipschitz unstable manifold of the periodic orbit exists at the grazing bifurcation point.",

keywords = "global manifold, grazing bifurcation",

author = "R Szalai and HM Osinga",

note = "Additional information: Submitted to the journal Nonlinearity ",

year = "2007",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Unstable manifolds of a limit cycle near grazing

AU - Szalai, R

AU - Osinga, HM

N1 - Additional information: Submitted to the journal Nonlinearity

PY - 2007

Y1 - 2007

N2 - We study the local dynamics of an impacting system near a grazing bifurcation point. In particular, we investigate local invariant manifolds of grazing periodic orbits. At a grazing bifurcation point the local return map does not have a Jacobian nor is of Lipschitz continuous, so that the classical theory does not apply. Nevertheless, we are able to use the Graph Transform technique and show that under certain conditions a local Lipschitz unstable manifold of the periodic orbit exists at the grazing bifurcation point.

AB - We study the local dynamics of an impacting system near a grazing bifurcation point. In particular, we investigate local invariant manifolds of grazing periodic orbits. At a grazing bifurcation point the local return map does not have a Jacobian nor is of Lipschitz continuous, so that the classical theory does not apply. Nevertheless, we are able to use the Graph Transform technique and show that under certain conditions a local Lipschitz unstable manifold of the periodic orbit exists at the grazing bifurcation point.

KW - global manifold

KW - grazing bifurcation

M3 - Working paper and Preprints

BT - Unstable manifolds of a limit cycle near grazing

ER -