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Miniaturized handheld Raman imager based on 2D MEMS scanning for non-destructive analysis of thermally sensitive samples. [PDF]
Biomed Opt ExpressZheng Y, Mu T.
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Visualization of Topological Structures in Area-Preserving Maps
IEEE Transactions on Visualization and Computer Graphics, 2011Area-preserving maps are found across a wide range of scientific and engineering problems. Their study is made challenging by the significant computational effort typically required for their inspection but more fundamentally by the fractal complexity of salient structures.
Christoph Garth +2 more
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Introduction to area preserving maps
Advanced Series in Nonlinear Dynamics, 1993exaly +2 more sources
The Multiplicity of Bifurcations for Area-Preserving Maps
Bulletin of the London Mathematical Society, 1994The authors study \(C^\infty\) one-parameter families of area-preserving mappings of \(\mathbb{R}^2\), \(f : \mathbb{R}^2 \times \mathbb{R} \to \mathbb{R}^2\). An elementary \(n\)-furcation occurs at a point \((x,\mu)\) such that \(x\) is a periodic point of least period \(p\) for \(f_\mu\), the eigenvalues of \(Df^p_\mu (x)\) are \(n\)-th roots of ...
Mackay, Robert S., Shardlow, Tony
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EFFECT OF PERTURBATION ON THE AREA PRESERVATION MAP
International Journal of Bifurcation and Chaos, 1994Subharmonic bifurcation patterns in area-preserving maps change their forms dramatically under dissipative perturbation. The studies of such changes are done by the use of the normal form theory and the Lyapunov-Schmidt reduction method where the eigenvalues of the linearized map move along a circle of radius (1−∊)1/2 in the complex plane. The results
WOO, HJ, LEE, EK Lee, Eok Kyun, KIM, YI
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Stability of an Area‐Preserving Mapping
Annals of the New York Academy of Sciences, 1987In many cases, the evolution of a Hamiltonian system can be represented by an area-preserving mapping of the plane onto itself. The stability or instability of the dynamical system is reflected in the derived mapping. The mappingT(x, y)=(x', y'): $$\begin{gathered} x\prime = x + a(y - y^3 ) \hfill \\ y\prime = y - a(x\prime - x\prime ^3 ) \hfill \\ \
Jenkins, B. Z., Bartlett, J. H.
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Area-preserving Poincar� mappings of the unit disk
Celestial Mechanics, 1987Summary: The best way to investigate the long-time behaviour of dynamical systems is to introduce an appropriate Poincaré mapping P and study its iterates. Two cases of physical interest arise: Conservative and dissipative systems. While the latter has been considered by a great many authors, much less is known for the first one (according to Liouville'
Neutsch, Wolfram, Kallrath, Josef
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Diffusion in models of modulated area-preserving maps
Physical Review A, 1992We investigate the diffusion in the action variable when the frequency of an integrable isochronous map is modulated. Purely stochastic, hyperbolic, or periodic deterministic modulations are considered. The diffusion coefficient in the invariant for the unperturbed map is exactly determined and shown to be nonzero, except in the last case, when the ...
A. Bazzani +3 more
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Organization of chaos in area-preserving maps
Physical Review Letters, 1990Summary: Chaos in area-preserving maps is organized on the basis of the unstable periodic orbits (UPOs) and the partition of phase space into resonances. Each UPO is of a well defined type, which specifies the sequence of resonances visited and the number of rotations performed in a resonance.
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