Reduction of Dietrich-Ruina attractors to unimodal maps

S. Shkoller (1) , J.-B. Minster (2)

1 Center for Nonlinear Studies MS-B258
2 IGPP - Institute of Geophysics and Planetary Physics [San Diego]

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.

Domaines: Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Astrophysique [astro-ph]; Sciences de la Terre

S. Shkoller, J.-B. Minster. Reduction of Dietrich-Ruina attractors to unimodal maps. Nonlinear Processes in Geophysics, 1997, 4 (2), pp.63-69. ⟨hal-00301843⟩