Abstract
In this chapter we state Hilbert’s 16th problem restricted to algebraic limit cycles. Namely, consider the set Σ’ n of all real polynomial vector fields \( \chi = \left( {P,\,Q} \right)\) of degree n having real irreducible \( \left( {{\rm on}\, \mathbb{R}\left[ {x,\,y} \right]} \right)\) invariant algebraic curves.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Llibre, J., Ramírez, R. (2016). Hilbert’s 16th Problem for Algebraic Limit Cycles. In: Inverse Problems in Ordinary Differential Equations and Applications. Progress in Mathematics, vol 313. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-26339-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-26339-7_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-26337-3
Online ISBN: 978-3-319-26339-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)