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• W4323341946 abstract "Using only elementary techniques we prove that for any $ C^r $ diffeomorphism, $ f $, of a compact manifold of dimension $ d>2 $, $ 1leq rleq infty $, admitting a transverse homoclinic intersection, we can find a $ C^1 $-open neighborhood of $ f $ containing a $ C^1 $-open and $ C^r $-dense set of $ C^r $ diffeomorphisms which have a periodic point with real and simple spectrum. We use this fact to prove that $ C^r $-generically among $ C^r $ diffeomorphisms with horseshoes, we have density of periodic points with real and simple spectrum inside the horseshoe. As a corollary, we obtain that generically in the $ C^1 $-topology the unique obstruction to the existence of periodic points with real and simple spectrum are the Morse-Smale diffeomorphisms with all the periodic points admitting non-real eigenvalues." @default.
• W4323341946 created "2023-03-08" @default.
• W4323341946 creator A5005912273 @default.
• W4323341946 creator A5008076091 @default.
• W4323341946 date "2023-01-01" @default.
• W4323341946 modified "2023-09-25" @default.
• W4323341946 title "Elementary proof for the existence of periodic points with real and simple spectrum for diffeomorphisms in any dimension" @default.
• W4323341946 cites W1975482467 @default.
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• W4323341946 doi "https://doi.org/10.3934/dcds.2023016" @default.
• W4323341946 hasPublicationYear "2023" @default.
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