Universal dynamics in a neighborhood of a generic elliptic periodic point

V. Gelfreich; D. Turaev

doi:10.1134/S156035471002005X

Universal dynamics in a neighborhood of a generic elliptic periodic point

V. Gelfreich, D. Turaev

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

14 Scopus citations

Abstract

We show that a generic area-preserving two-dimensional map with an elliptic periodic point is C^ω-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.

Original language	English
Pages (from-to)	159-164
Number of pages	6
Journal	Regular and Chaotic Dynamics
Volume	15
Issue number	2
DOIs	https://doi.org/10.1134/S156035471002005X
State	Published - 1 Jan 2010
Externally published	Yes

Keywords

Area-preserving map
Exponentially small splitting
Hamiltonian system
Homoclinic tangency
KAM theory
Newhouse phenomenon
Volume-preserving flow
Wild hyperbolic set

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1134/S156035471002005X

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title = "Universal dynamics in a neighborhood of a generic elliptic periodic point",

abstract = "We show that a generic area-preserving two-dimensional map with an elliptic periodic point is Cω-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.",

keywords = "Area-preserving map, Exponentially small splitting, Hamiltonian system, Homoclinic tangency, KAM theory, Newhouse phenomenon, Volume-preserving flow, Wild hyperbolic set",

author = "V. Gelfreich and D. Turaev",

note = "Funding Information: This work was supported by the Leverhulme Foundation and by ISF grant 273/07. The authors are grateful to Gonchenko and Shilnikov for useful discussions.",

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AU - Gelfreich, V.

AU - Turaev, D.

N1 - Funding Information: This work was supported by the Leverhulme Foundation and by ISF grant 273/07. The authors are grateful to Gonchenko and Shilnikov for useful discussions.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We show that a generic area-preserving two-dimensional map with an elliptic periodic point is Cω-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.

AB - We show that a generic area-preserving two-dimensional map with an elliptic periodic point is Cω-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.

KW - Area-preserving map

KW - Exponentially small splitting

KW - Hamiltonian system

KW - Homoclinic tangency

KW - KAM theory

KW - Newhouse phenomenon

KW - Volume-preserving flow

KW - Wild hyperbolic set

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DO - 10.1134/S156035471002005X

M3 - Article

AN - SCOPUS:77951899662

SN - 1560-3547

VL - 15

SP - 159

EP - 164

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

IS - 2

ER -

Universal dynamics in a neighborhood of a generic elliptic periodic point

Abstract

Keywords

ASJC Scopus subject areas

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