Search on the brink of chaos

The linear search problem is studied from the view point of Hamiltonian dynamics. For the specific, yet representative case of exponentially distributed position of the hidden object, it is shown that the optimal orbit follows an unstable separatrix in the associated Hamiltonian system.

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Bibliographic Details
Published in:Nonlinearity 2012-11, Vol.25 (11), p.3023-3047
Main Authors: Baryshnikov, Yu, Zharnitsky, V
Format: Article
Language:English
Subjects:
Chaos theory
Dynamic tests
Dynamical systems
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical methods in physics
Mathematics
Nonlinear dynamics
Nonlinearity
Optimization
Orbits
Other topics in mathematical methods in physics
Physics
Sciences and techniques of general use
Searching
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Description
Summary:The linear search problem is studied from the view point of Hamiltonian dynamics. For the specific, yet representative case of exponentially distributed position of the hidden object, it is shown that the optimal orbit follows an unstable separatrix in the associated Hamiltonian system.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/25/11/3023