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Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry

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Control and Chaos

Part of the book series: Mathematical Modelling ((MMO,volume 8))

Abstract

The structure of the differential or difference equations used to model a complex real-life system should reflect some of the underlying symmetries of the system. Characterising and exploiting this structure can lead to better prediction and explanation of the motion. For example, a well-studied structure is that found in Hamiltonian or conservative dynamical systems. In this paper, we survey our work on dynamical systems with another type of structure, namely a (generalised) time-reversal symmetry. We explain some of the dynamical consequences and structure arising from this property. We explore the question of how systems with this (generalized) time-reversal symmetry are similar to, and how they differ from, Hamiltonian dynamical systems. We pay particular attention to low-dimensional (2D and 3D) systems and use specific examples to illustrate our points.

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Author information

Authors and Affiliations

  1. Department of Mathematics, La Trobe University, Bundoora, 3083, VIC, Australia

    John A. G. Roberts

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  1. John A. G. Roberts
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Editor information

Editors and Affiliations

  1. Center for Applied Dynamics and Optimization, Department of Mathematics, The University of Western Australia, 6907, Perth, Australia

    Kevin Judd , Alistair Mees  & Kok Lay Teo ,  & 

  2. Aerospace and Mechanical Engineering, University of Arizona, 85721, Tucson, Arizona, USA

    Thomas L. Vincent

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© 1997 Birkhäuser Boston

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Roberts, J.A.G. (1997). Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry. In: Judd, K., Mees, A., Teo, K.L., Vincent, T.L. (eds) Control and Chaos. Mathematical Modelling, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2446-4_7

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  • DOI: https://doi.org/10.1007/978-1-4612-2446-4_7

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7540-4

  • Online ISBN: 978-1-4612-2446-4

  • eBook Packages: Springer Book Archive

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