• Corpus ID: 1177415

On the thermodynamics of curves and other curlicues

@inproceedings{Moore1989OnTT,
  title={On the thermodynamics of curves and other curlicues},
  author={R. R. Moore and A.J. van der Poorten},
  year={1989}
}
maths-proceedings.anu.edu.au
16 Citations
Background Citations
10
Methods Citations
1

16 Citations

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The Journal of Fourier Analysis and Applications

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Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems

According to the proposed method all linear dynamical systems evolve at constant zero entropy, while higher asymptotic values characterise nonlinear systems, in which case it has common features with other classic approaches.

Limiting curlicue measures for theta sums

We consider the ensemble of curves $\{\gamma_{\alpha,N}:\alpha\in(0,1],N\in\N\}$ obtained by linearly interpolating the values of the normalized theta sum $N^{-1/2}\sum_{n=0}^{N'-1}\exp(\pi i…

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A generalisation of the entropy of a plane curve to ¿n space is provided and the generalised entropy is used to evaluate the nonlinear behaviour of dynamical systems. The entropy of a curve, first…

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This work investigates the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation--a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space and describes an efficient approach for a deterministic enumeration of ring conformations.

References

Renormalisation of curlicues

The recursively spiralling patterns drawn in the complex plane by the values of SL( tau )= Sigma Ln=1 exp(i pi tau n2) as L to infinity with tau fixed in the range 0<or= tau <or=1, depend on the…