# American Institute of Mathematical Sciences

April  2013, 6(4): 1017-1027. doi: 10.3934/dcdss.2013.6.1017

## On a structure of the fixed point set of homogeneous maps

 1 Department of Mathematics 2 Bar-Ilan University 3 Ramat-Gan, 52900

Received  June 2011 Revised  September 2011 Published  December 2012

A spectral and inverse spectral problem for homogeneous polynomial maps is discussed.The $m$-independence of vectors based on the symmetric tensor powers performs as a main toolto study the structure of the spectrum. Possible restrictions on this structureare described in terms of syzygies provided by the Euler-Jacobi formula.Applications to projective dynamics are discussed.
Citation: Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017
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