| EPSRC Reference: |
GR/S98986/01 |
| Title: |
Developing Efficient Method for Locating Periodic Orbits in Hamiltonian Maps and Flows |
| Principal Investigator: |
Davidchack, Professor R |
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| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 May 2004 |
Ends: |
30 April 2007 |
Value (£): |
66,475
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Non-linear Systems Mathematics |
| Numerical Analysis |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The knowledge of location and stability properties of periodic orbits embedded in chaotic dynamics is essential for understanding the behavior of nonlinear systems. Many theoretical and experimental tools have been developed to characterise the properties of chaotic systems in terms of periodic orbits. However, the utility of these tools is often limited by the difficulty of locating periodic orbits in such systems. The proposed research will be devoted to the development of an algorithm for an efficient detection of periodic orbits in nonlinear systems in general, as well as an optimised algorithm for Hamiltonian maps and flows. As a starting point, the project will use a recently proposed technique for locating unstable periodic orbits by transforming the dynamical system into a set of associated systems with the same number and location of periodic orbits, but which are stabilised by the transformations. The research will focus on studying the properties of the stabilising transformations with the goal of developing an efficient detection algorithm applicable to a variety of Hamiltonian systems with a special emphasis on higher-dimensional systems. The resulting algorithm will greatly enhance the utility of theoretical and experimental tools that employ periodic orbits to study nonlinear dynamics.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.le.ac.uk |