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arXiv · 1301.2364

On the Arnold's conjecture on hyperbolic homogeneous polynomials

Adriana Ortiz-Rodríguez·Federico Sánchez-Bringas
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Abstract

The Hessian Topology is a subject with interesting relations with some classical problems of analysis and geometry. In this article we prove a conjecture on this subject stated by V.I. Arnold concerning the number of connected components of hyperbolic homogeneous polynomials of degree $n$. The proof is constructive and provides models. Our approach uses index properties at isolated singularities of hyperbolic quadratic differential forms and combinatorial properties of recurrent functions.

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Adriana Ortiz-Rodríguez, Federico Sánchez-Bringas. 2013-01-11. On the Arnold's conjecture on hyperbolic homogeneous polynomials. https://arxiv.org/abs/1301.2364

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