Matches in SemOpenAlex for { <https://semopenalex.org/work/W2000849354> ?p ?o ?g. }
Showing items 1 to 93 of
93
with 100 items per page.
- W2000849354 abstract "It is well known that the stability of a homoclinic loop for planar vector fields is closely related to the cyclicity of this homoclinic loop. For a planar homoclinic loop consisting of a hyperbolic saddle, the loop values are crucial to the stability. The loop values are divided into two classes: saddle values and separatrix values. The saddle values are related to Dulac map near the saddle, and the separatrix values are related to the regular map near the homoclinic loop. The alternation of these quantities determines the stability of the homoclinic loop. So, it is important to investigate the separatrix values in both theory and for practical applications. For a given planar vector field, we can try to calculate the saddle values by means of dual Liapunov constants or by finding elementary invariants developed by Liu and Li [1990]. The first separatrix value was obtained by Dulac. The second separatrix value was given by Han and Zhu [2007] and by Hu and Feng [2001] independently. The third separatrix value was obtained by Luo and Li [2005] by means of Tkachev's method. In this paper, we shall establish the formulae for the third and fourth separatrix values. As applications, we will give an example with the homoclinic bifurcation of order 9 and prove that the cyclicity of homoclinic loop together with double homoclinic loops is 57." @default.
- W2000849354 created "2016-06-24" @default.
- W2000849354 creator A5042024059 @default.
- W2000849354 creator A5081848844 @default.
- W2000849354 date "2009-07-01" @default.
- W2000849354 modified "2023-09-24" @default.
- W2000849354 title "THE SEPARATRIX VALUES OF A PLANAR HOMOCLINIC LOOP" @default.
- W2000849354 cites W1564263151 @default.
- W2000849354 cites W1975136536 @default.
- W2000849354 cites W2009734469 @default.
- W2000849354 cites W2017348434 @default.
- W2000849354 cites W2042498362 @default.
- W2000849354 cites W2049815318 @default.
- W2000849354 cites W2061809639 @default.
- W2000849354 cites W2069228691 @default.
- W2000849354 cites W2077189269 @default.
- W2000849354 cites W2078522451 @default.
- W2000849354 cites W2142664960 @default.
- W2000849354 doi "https://doi.org/10.1142/s0218127409024037" @default.
- W2000849354 hasPublicationYear "2009" @default.
- W2000849354 type Work @default.
- W2000849354 sameAs 2000849354 @default.
- W2000849354 citedByCount "2" @default.
- W2000849354 countsByYear W20008493542012 @default.
- W2000849354 countsByYear W20008493542018 @default.
- W2000849354 crossrefType "journal-article" @default.
- W2000849354 hasAuthorship W2000849354A5042024059 @default.
- W2000849354 hasAuthorship W2000849354A5081848844 @default.
- W2000849354 hasConcept C112972136 @default.
- W2000849354 hasConcept C114614502 @default.
- W2000849354 hasConcept C119857082 @default.
- W2000849354 hasConcept C121332964 @default.
- W2000849354 hasConcept C121684516 @default.
- W2000849354 hasConcept C126255220 @default.
- W2000849354 hasConcept C134306372 @default.
- W2000849354 hasConcept C134786449 @default.
- W2000849354 hasConcept C155405617 @default.
- W2000849354 hasConcept C158622935 @default.
- W2000849354 hasConcept C184670325 @default.
- W2000849354 hasConcept C200581526 @default.
- W2000849354 hasConcept C2777127463 @default.
- W2000849354 hasConcept C2781349735 @default.
- W2000849354 hasConcept C33923547 @default.
- W2000849354 hasConcept C41008148 @default.
- W2000849354 hasConcept C62520636 @default.
- W2000849354 hasConcept C76379757 @default.
- W2000849354 hasConcept C82706917 @default.
- W2000849354 hasConceptScore W2000849354C112972136 @default.
- W2000849354 hasConceptScore W2000849354C114614502 @default.
- W2000849354 hasConceptScore W2000849354C119857082 @default.
- W2000849354 hasConceptScore W2000849354C121332964 @default.
- W2000849354 hasConceptScore W2000849354C121684516 @default.
- W2000849354 hasConceptScore W2000849354C126255220 @default.
- W2000849354 hasConceptScore W2000849354C134306372 @default.
- W2000849354 hasConceptScore W2000849354C134786449 @default.
- W2000849354 hasConceptScore W2000849354C155405617 @default.
- W2000849354 hasConceptScore W2000849354C158622935 @default.
- W2000849354 hasConceptScore W2000849354C184670325 @default.
- W2000849354 hasConceptScore W2000849354C200581526 @default.
- W2000849354 hasConceptScore W2000849354C2777127463 @default.
- W2000849354 hasConceptScore W2000849354C2781349735 @default.
- W2000849354 hasConceptScore W2000849354C33923547 @default.
- W2000849354 hasConceptScore W2000849354C41008148 @default.
- W2000849354 hasConceptScore W2000849354C62520636 @default.
- W2000849354 hasConceptScore W2000849354C76379757 @default.
- W2000849354 hasConceptScore W2000849354C82706917 @default.
- W2000849354 hasLocation W20008493541 @default.
- W2000849354 hasOpenAccess W2000849354 @default.
- W2000849354 hasPrimaryLocation W20008493541 @default.
- W2000849354 hasRelatedWork W1837094555 @default.
- W2000849354 hasRelatedWork W1964759045 @default.
- W2000849354 hasRelatedWork W1978541442 @default.
- W2000849354 hasRelatedWork W1988566766 @default.
- W2000849354 hasRelatedWork W1999831408 @default.
- W2000849354 hasRelatedWork W2001232314 @default.
- W2000849354 hasRelatedWork W2039299540 @default.
- W2000849354 hasRelatedWork W2042172743 @default.
- W2000849354 hasRelatedWork W2042800579 @default.
- W2000849354 hasRelatedWork W2051994009 @default.
- W2000849354 hasRelatedWork W206547127 @default.
- W2000849354 hasRelatedWork W2077398926 @default.
- W2000849354 hasRelatedWork W2082192588 @default.
- W2000849354 hasRelatedWork W2142664960 @default.
- W2000849354 hasRelatedWork W2316492659 @default.
- W2000849354 hasRelatedWork W2373389541 @default.
- W2000849354 hasRelatedWork W2559520563 @default.
- W2000849354 hasRelatedWork W2738971580 @default.
- W2000849354 hasRelatedWork W2885969990 @default.
- W2000849354 hasRelatedWork W2943888718 @default.
- W2000849354 isParatext "false" @default.
- W2000849354 isRetracted "false" @default.
- W2000849354 magId "2000849354" @default.
- W2000849354 workType "article" @default.