Reduction of Dietrich-Ruina attractors to unimodal maps

Shkoller, S.; Minster, J.-B.

doi:https://doi.org/10.5194/npg-4-63-1997

Articles | Volume 4, issue 2

Nonlin. Processes Geophys., 4, 63–69, 1997

https://doi.org/10.5194/npg-4-63-1997

© Author(s) 1997. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Nonlin. Processes Geophys., 4, 63–69, 1997

https://doi.org/10.5194/npg-4-63-1997

© Author(s) 1997. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Articles | Volume 4, issue 2

30 Jun 1997

Reduction of Dietrich-Ruina attractors to unimodal maps

S. Shkoller¹ and J.-B. Minster² S. Shkoller and J.-B. Minster S. Shkoller¹ and J.-B. Minster²

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¹Center for Nonlinear Studies MS-B258, Los Alamos National Laboratory, Los Alamos, NM 87545
²Institute of Geophysics and Planetary Physics, University of California at San Diego, La Jolia, CA 92093-0225

Abstract. We present a geometric analysis of a quasi-static single degree of freedom elastic slider with a state and rate dependent friction law. In particular, we examine and characterize the regime of chaotic motions displayed by the Dieterich-Ruina model. We do so by numerically reducing the chaotic attractors to a family of unimodal maps and discuss why this suggests complex behaviour in the dynamical system.