Bifurcations of Limit Cycles and Critical Periods

Valery Romanovski () and Douglas Shafer ()
Additional contact information
Valery Romanovski: University of Maribor, Center for Applied Mathematics & Theorectical Physics
Douglas Shafer: University of North Carolina, Mathematics Dept.

Chapter Chapter 6 in The Center and Cyclicity Problems, 2009, pp 1-57 from Springer

Abstract: In this chapter we consider systems of ordinary differential equations of the form 6.1 $$\dot u = \tilde U(u,v), \quad \dot v = \tilde V(u,v),$$ where u and v are real variables and $\tilde U(u,v)$ and $\tilde V(u,v)$ are polynomials for which max(deg, $\tilde U$ deg $\tilde V$ ) ≤ n. The second part of the sixteenth of Hilbert’s well-known list of open problems posed in the year 1900 asks for a description of the possible number and relative locations of limit cycles (isolated periodic orbits) occurring in the phase portrait of such polynomial systems. The minimal uniform bound H (n) on the number of limit cycles for systems (6.1) (for some ӿxed n) is now known as the nth Hilbert number.

Keywords: Phase Portrait; Critical Period; Polynomial System; Minimal Basis; Quadratic System (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4727-8_6

Ordering information: This item can be ordered from
http://www.springer.com/9780817647278

DOI: 10.1007/978-0-8176-4727-8_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().