Let F : Kn → Kn be a polynomial map such that F-1(0) is compact, where K = R or C. Then we give a condition implying that there is a uniform bound for the Łojasiewicz exponent at infinity in certain deformations of F. This fact gives a result about the invariance of the global index of F.
Bibliographical noteFunding Information:
The first author was partially supported by DGICYT Grant MTM2012-33073 . The second author was partially supported by FAPESP-BEPE 2012/22365-8 .
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- Newton polyhedron
- Polynomial vector fields
- Topological index
- Łojasiewicz exponent at infinity