Taiwanese Journal of Mathematics

$\mathcal{C}^{1}$ SELF-MAPS ON $\mathbb{S}^{n}$, $\mathbb{S}^{n}\times \mathbb{S}^{m}$, $\mathbb{C}$P$^{n}$ AND $\mathbb{H}$P$^{n}$ WITH ALL THEIR PERIODIC ORBITS HYPERBOLIC

Juan Luis García Guirao and Jaume Llibre

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Abstract

We study in its homological class the periodic structure of the $\mathcal{C}^{1}$ self$-$maps on the manifolds $\mathbb{S}^{n}$ (the $n-$dimensional sphere), $\mathbb{S}^{n}\times \mathbb{S}^{m}$ (the product space of the $n-$dimensional with the $m-$dimensional spheres), $\mathbb{C}$P$^{n}$ (the $n-$dimensional complex projective space) and $\mathbb{H}$P$^{n}$ (the $n-$dimensional quaternion projective space), having all their periodic orbits hyperbolic.

Article information

Source
Taiwanese J. Math., Volume 16, Number 1 (2012), 323-334.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406543

Digital Object Identifier
doi:10.11650/twjm/1500406543

Mathematical Reviews number (MathSciNet)
MR2887867

Zentralblatt MATH identifier
1243.37023

Subjects
Primary: 37C05: Smooth mappings and diffeomorphisms 37C25: Fixed points, periodic points, fixed-point index theory 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems

Keywords
hyperbolic periodic point period Lefschetz zeta function Lefschetz number sphere complex projective space quaternion projective space

Citation

García Guirao, Juan Luis; Llibre, Jaume. $\mathcal{C}^{1}$ SELF-MAPS ON $\mathbb{S}^{n}$, $\mathbb{S}^{n}\times \mathbb{S}^{m}$, $\mathbb{C}$P$^{n}$ AND $\mathbb{H}$P$^{n}$ WITH ALL THEIR PERIODIC ORBITS HYPERBOLIC. Taiwanese J. Math. 16 (2012), no. 1, 323--334. doi:10.11650/twjm/1500406543. https://projecteuclid.org/euclid.twjm/1500406543


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