Dynamical Collapse of Trajectories Part I: Homoclinic Tangles in Systems with Dry Friction

J. J. B. Biemond; A. P. S. de Moura; C. Grebogi; N. van de Wouw; H. Nijmeijer

Dynamical Collapse of Trajectories Part I: Homoclinic Tangles in Systems with Dry Friction

J. J. B. Biemond, A. P. S. de Moura, C. Grebogi, N. van de Wouw, H. Nijmeijer

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

Abstract

Dry friction induces unexpected dynamical behaviour, causing distinct trajectories to collapse onto a single point in finite time. The result is that transversal homoclinic orbits generate chaotic saddles with forward dynamics that is qualitatively different from the backward dynamics. The space of initial conditions converging to the chaotic saddle is fractal, but the set of points diverging from it is not: friction destroys the complexity of the forward dynamics by generating a unique horseshoe-like topology.

Original language	English
Title of host publication	Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC 2014)
Publisher	Vienna University of Technology
Number of pages	2
ISBN (Print)	978-3-200-03433-4
Publication status	Published - 2014
Event	8th European Nonlinear Dynamics Conference: (ENOC 2014) - Vienna, Austria Duration: 6 Jul 2014 → 11 Jul 2014

Conference

Conference	8th European Nonlinear Dynamics Conference
Country/Territory	Austria
City	Vienna
Period	6/07/14 → 11/07/14

Cite this

Dynamical Collapse of Trajectories Part I : Homoclinic Tangles in Systems with Dry Friction. / Biemond, J. J. B.; de Moura, A. P. S.; Grebogi, C. et al.

Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC 2014). Vienna University of Technology, 2014. 345.

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

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abstract = "Dry friction induces unexpected dynamical behaviour, causing distinct trajectories to collapse onto a single point in finite time. The result is that transversal homoclinic orbits generate chaotic saddles with forward dynamics that is qualitatively different from the backward dynamics. The space of initial conditions converging to the chaotic saddle is fractal, but the set of points diverging from it is not: friction destroys the complexity of the forward dynamics by generating a unique horseshoe-like topology.",

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T2 - 8th European Nonlinear Dynamics Conference

AU - Biemond, J. J. B.

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AU - Grebogi, C.

AU - van de Wouw, N.

AU - Nijmeijer, H.

PY - 2014

Y1 - 2014

N2 - Dry friction induces unexpected dynamical behaviour, causing distinct trajectories to collapse onto a single point in finite time. The result is that transversal homoclinic orbits generate chaotic saddles with forward dynamics that is qualitatively different from the backward dynamics. The space of initial conditions converging to the chaotic saddle is fractal, but the set of points diverging from it is not: friction destroys the complexity of the forward dynamics by generating a unique horseshoe-like topology.

AB - Dry friction induces unexpected dynamical behaviour, causing distinct trajectories to collapse onto a single point in finite time. The result is that transversal homoclinic orbits generate chaotic saddles with forward dynamics that is qualitatively different from the backward dynamics. The space of initial conditions converging to the chaotic saddle is fractal, but the set of points diverging from it is not: friction destroys the complexity of the forward dynamics by generating a unique horseshoe-like topology.

UR - http://enoc2014.conf.tuwien.ac.at/index.php/14-minisymposia/49-ms-10

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M3 - Published conference contribution

SN - 978-3-200-03433-4

BT - Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC 2014)

PB - Vienna University of Technology

Y2 - 6 July 2014 through 11 July 2014

ER -

Dynamical Collapse of Trajectories Part I: Homoclinic Tangles in Systems with Dry Friction

Abstract

Conference

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