Abstract
In many cases, given a non-linear map, linearized systems near its fixed points do qualitatively capture its topological and algebraic properties. This suggests to extend the linear spectral theory to non-linear operators by considering spectra of linearizations in small neighborhoods of the fixed points. In the present paper, we develop this approach for quadratic maps. Several standard concepts such as asymptotic laws for splitting/gluing zeros of polynomial maps) are considered from new (and, possibly, unexpected) angles.
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The author wishes to cordially thank the referee for various suggestions and comments that enable to make many important corrections and to significantly improve the presentation of the paper.
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Krasnov, Y. (2019). Spectral Theory for Nonlinear Operators: Quadratic Case. In: Karapetyants, A., Kravchenko, V., Liflyand, E. (eds) Modern Methods in Operator Theory and Harmonic Analysis. OTHA 2018. Springer Proceedings in Mathematics & Statistics, vol 291. Springer, Cham. https://doi.org/10.1007/978-3-030-26748-3_12
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DOI: https://doi.org/10.1007/978-3-030-26748-3_12
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