Dimension estimate of the global attractor for forced oscillation systems

Yuji Hattori; Naoyuki Ishimura; Isamu Ohnishi; Makoto Umeki

doi:10.1007/BF03167279

Dimension estimate of the global attractor for forced oscillation systems

Yuji Hattori, Naoyuki Ishimura, Isamu Ohnishi, Makoto Umeki

IFS - Complex Flow Research Division

The University of Tokyo

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

1 Citation (Scopus)

Abstract

We deal with the largest compact invariant set X for forced oscillation systems. As in the Lorenz system X may contain a strange attractor. Invoking the Kaplan-Yorke formula we give an upper bound for the dimension of X analytically and compare it with numerical results. It is, observed that both agree rather well when the damping coefficient is small.

Original language	English
Pages (from-to)	351-366
Number of pages	16
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	10
Issue number	3
DOIs	https://doi.org/10.1007/BF03167279
Publication status	Published - 1993 Oct

Keywords

dimensions
forced oscillation systems
Kaplan-Yorke formula
strange attractor

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10.1007/BF03167279

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abstract = "We deal with the largest compact invariant set X for forced oscillation systems. As in the Lorenz system X may contain a strange attractor. Invoking the Kaplan-Yorke formula we give an upper bound for the dimension of X analytically and compare it with numerical results. It is, observed that both agree rather well when the damping coefficient is small.",

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author = "Yuji Hattori and Naoyuki Ishimura and Isamu Ohnishi and Makoto Umeki",

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N2 - We deal with the largest compact invariant set X for forced oscillation systems. As in the Lorenz system X may contain a strange attractor. Invoking the Kaplan-Yorke formula we give an upper bound for the dimension of X analytically and compare it with numerical results. It is, observed that both agree rather well when the damping coefficient is small.

AB - We deal with the largest compact invariant set X for forced oscillation systems. As in the Lorenz system X may contain a strange attractor. Invoking the Kaplan-Yorke formula we give an upper bound for the dimension of X analytically and compare it with numerical results. It is, observed that both agree rather well when the damping coefficient is small.

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Dimension estimate of the global attractor for forced oscillation systems

Abstract

Keywords

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