elliptic%20umbilic%20catastrophe

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1: 36.4 Bifurcation Sets

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Critical Points for Umbilics

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Bifurcation (Catastrophe) Set for Umbilics

… ►Elliptic umbilic bifurcation set (codimension three): for fixed $z$, the section of the bifurcation set is a three-cusped astroid … ►Elliptic umbilic cusp lines (ribs): … ►

§36.4(ii) Visualizations

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2: 36.5 Stokes Sets

… ►Stokes sets are surfaces (codimension one) in $𝐱$ space, across which ${\mathrm{\Psi }}_K(𝐱;k)$ or ${\mathrm{\Psi }}^{(\mathrm{U})}(𝐱;k)$ acquires an exponentially-small asymptotic contribution (in $k$), associated with a complex critical point of ${\mathrm{\Phi }}_K$ or . … ►

§36.5(iii) Umbilics

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Elliptic Umbilic Stokes Set (Codimension three)

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Figure 36.5.5: Elliptic umbilic catastrophe with $z=\mathrm{constant}$. Magnify

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3: Bibliography B

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Stokes surfaces of diffraction catastrophes with codimension three. Nonlinearity 3 (2), pp. 281–291.

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External Links:

ISSN 0951-7715, Document, MathReview (Maria Carmen Romero-Fuster), ZentralBlatt

Referenced by:

§36.2(i), §36.5(ii), §36.5(iii), §36.5(iv).

Encodings:

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Overlapping Stokes smoothings: Survival of the error function and canonical catastrophe integrals. Proc. Roy. Soc. London Ser. A 444, pp. 201–216.

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External Links:

ISSN 0962-8444, FullText, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§36.12(iii).

Encodings:

BibTeX

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Axial and focal-plane diffraction catastrophe integrals. J. Phys. A 43 (37), pp. 375206, 13.

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External Links:

ISSN 1751-8113, Document, FullText, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

(36.2.28), (36.2.29), §36.2(iv).

Encodings:

BibTeX

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The elliptic umbilic diffraction catastrophe. Phil. Trans. Roy. Soc. Ser. A 291 (1382), pp. 453–484.

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External Links:

FullText

Referenced by:

§36.15(iv), §36.2(i), §36.7(ii), §36.7(iii).

Encodings:

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Catastrophe optics: Morphologies of caustics and their diffraction patterns. In Progress in Optics, E. Wolf (Ed.), Vol. 18, pp. 257–346.

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Referenced by:

§36.14(ii), Ch.36.

Encodings:

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