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Bifurcations of the global stable set of a planar endomorphism near a cusp singularity (2008)
Journal Article
Hobbs, C., & Osinga, H. (2008). Bifurcations of the global stable set of a planar endomorphism near a cusp singularity. International Journal of Bifurcation and Chaos, 18(8), 2207-2222. https://doi.org/10.1142/S021812740802166X

The dynamics of a system defined by an endomorphism is essentially different from that of a system defined by a diffeomorphism due to interaction of invariant objects with the so-called critical locus. A planar endomorphism typically folds the phase... Read More about Bifurcations of the global stable set of a planar endomorphism near a cusp singularity.

Theory and numerical evaluation of oddoids and evenoids: Oscillatory cuspoid integrals with odd and even polynomial phase functions (2007)
Journal Article
Kirk, N. P., Connor, J., & Hobbs, C. (2007). Theory and numerical evaluation of oddoids and evenoids: Oscillatory cuspoid integrals with odd and even polynomial phase functions. Journal of Computational and Applied Mathematics, 207(2), 192-213. https://doi.org/10.1016/j.cam.2006.10.079

The properties of oscillating cuspoid integrals whose phase functions are odd and even polynomials are investigated. These integrals are called oddoids and evenoids, respectively (and collectively, oddenoids). We have studied in detail oddenoids whos... Read More about Theory and numerical evaluation of oddoids and evenoids: Oscillatory cuspoid integrals with odd and even polynomial phase functions.