Volume 10:
The 12th International Workshop on Real and Complex Singularities, 22-27th July, 2012, Celebrating the 60th birthday of Prof. Shyuichi Izumiya, ICMC-USP, São Carlos, Brazil


Preface i
Editors: Osamu Saeki, V. H. Jorge Pérez, Takashi Nishimura, and R. Araújo dos Santos

Geometry and Singularities of the Prony mapping 1
Dmitry Batenkov and Yosef Yomdin

Naive motivic Donaldson--Thomas type Hirzebruch classes and some problems 26
Vittoria Bussi and Shoji Yokura

On regularity conditions at infinity 54
L. R. G. Dias

Singularities of affine equidistants: projections and contacts 67
W. Domitrz, P. de M. Rios, and M. A. S. Ruas

Some notes on the Euler obstruction of a function 82
Nicolas Dutertre and Nivaldo G. Grulha Jr.

Evolutes of fronts in the Euclidean plane 92
T. Fukunaga and M. Takahashi

The genericity of the infinitesimal Lipschitz condition for hypersurfaces 108
Terence Gaffney

Axiumbilic Singular Points on Surfaces Immersed in R^4 and their Generic Bifurcations 124
R. Garcia, J. Sotomayor, and F. Spindola

On the Euler characteristic of real Milnor fibres 147
Helmut A. Hamm

Lightlike hypersurfaces along spacelike submanifolds in de Sitter space 157
Shyuichi Izumiya and Takami Sato

Links of singularities up to regular homotopy 174
A. Katanaga, A. Némethi, and A. Szűcs

Periodic solutions of discontinuous second order differential systems 183
Jaume Llibre and Marco Antonio Teixeira

Abelian singularities of holomorphic Lie-foliations 191
Albetã Mafra and Bruno Scárdua

Some remarks about the topology of corank 2 map germs from R^2 to R^2 200
J.A. Moya-Pérez and J.J. Nuño-Ballesteros

Lipschitz geometry of complex curves 225
Walter D Neumann and Anne Pichon

The right classification of univariate power series in positive characteristic 235
Nguyen Hong Duc

The Geometry of Double Fold Maps 250
G. Peñafort-Sanchis

Koenderink type theorems for fronts 264
Kentaro Saji

Classifications of completely integrable implicit second order ordinary differential equations 271
Masatomo Takahashi

Lips and swallow-tails of singularities of product maps 286
Kazuto Takao