Uncertainty in the dynamics of conservative maps

Oliver Junge; Jerrold E. Marsden; Igor Mezic

doi:10.1109/cdc.2004.1430379

Uncertainty in the dynamics of conservative maps

Oliver Junge
, Jerrold E. Marsden
, Igor Mezic

Research output: Contribution to journal › Conference article › peer-review

23 Scopus citations

Abstract

This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R² to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.

Original language	English
Article number	WeB12.1
Pages (from-to)	2225-2230
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2
DOIs	https://doi.org/10.1109/cdc.2004.1430379
State	Published - 2004
Externally published	Yes
Event	2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas Duration: 14 Dec 2004 → 17 Dec 2004

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10.1109/cdc.2004.1430379

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abstract = "This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R2 to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.",

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AU - Marsden, Jerrold E.

AU - Mezic, Igor

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AB - This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R2 to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.

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DO - 10.1109/cdc.2004.1430379

M3 - Conference article

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EP - 2230

JO - Proceedings of the IEEE Conference on Decision and Control

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T2 - 2004 43rd IEEE Conference on Decision and Control (CDC)

Y2 - 14 December 2004 through 17 December 2004

ER -

Uncertainty in the dynamics of conservative maps

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