Matches in SemOpenAlex for { <https://semopenalex.org/work/W2126266600> ?p ?o ?g. }
Showing items 1 to 92 of
92
with 100 items per page.
- W2126266600 endingPage "61" @default.
- W2126266600 startingPage "11" @default.
- W2126266600 abstract "We consider the Lotka-Volterra Equations $$dot x = x(1 + ax + by), dot y = y( - lambda + cx + dy),$$ with λ a non negative number. Our aim is to understand the mechanisms which lead to the origin being linearizable, integrable or normalizable. In the case of integrability and linearizability, there is a natural dichotomy. When the system has an invariant line other than the axes, then the system is integrable and we give necessary and sufficient conditions for linearizability in this case. When there is no such line, then the conditions for linearizability and integrability are the same. In this case we show that the monodromy groups of the separatrices play a key role. In particular for λ=p/q withp+q ≤12 and λ=n/2,2/n withn∈N the origin is linearizable if and only if the monodromy groups can be shown to be linearizable by elementary arguments. We give 4 classes of these conditions, and their duals, in terms of the parameters of the system, and conjecture that these, together with two exceptional cases of Darboux linearizability, are the only integrability mechanisms for rational values of λ. The work on normalizability is more tentative. We give some sufficient conditions for this via monodromy groups, and give a complete classification when λ=0. We also investigate in detail the case λ=1, witha+c=0. Much of our ideas here are based on recent work on the unfolding of the Ecalle-Voronin modulus of analytic classification [13]. In particular we give examples of “half-normalizable” systems as well as an experimental example of a “transcritical bifurcation” of the functional moduli associated to the critical point." @default.
- W2126266600 created "2016-06-24" @default.
- W2126266600 creator A5012415802 @default.
- W2126266600 creator A5062305450 @default.
- W2126266600 date "2004-03-01" @default.
- W2126266600 modified "2023-10-13" @default.
- W2126266600 title "Normalizable, integrable and linearizable saddle points in the lotka-volterra system" @default.
- W2126266600 cites W1025151484 @default.
- W2126266600 cites W1499489219 @default.
- W2126266600 cites W1975797146 @default.
- W2126266600 cites W1988842480 @default.
- W2126266600 cites W1990163022 @default.
- W2126266600 cites W2003782300 @default.
- W2126266600 cites W2029282181 @default.
- W2126266600 cites W2040566154 @default.
- W2126266600 cites W2095621229 @default.
- W2126266600 cites W2156924128 @default.
- W2126266600 cites W2353020053 @default.
- W2126266600 cites W2493746692 @default.
- W2126266600 cites W2790950633 @default.
- W2126266600 doi "https://doi.org/10.1007/bf02968129" @default.
- W2126266600 hasPublicationYear "2004" @default.
- W2126266600 type Work @default.
- W2126266600 sameAs 2126266600 @default.
- W2126266600 citedByCount "42" @default.
- W2126266600 countsByYear W21262666002012 @default.
- W2126266600 countsByYear W21262666002013 @default.
- W2126266600 countsByYear W21262666002014 @default.
- W2126266600 countsByYear W21262666002015 @default.
- W2126266600 countsByYear W21262666002016 @default.
- W2126266600 countsByYear W21262666002017 @default.
- W2126266600 countsByYear W21262666002018 @default.
- W2126266600 countsByYear W21262666002019 @default.
- W2126266600 countsByYear W21262666002020 @default.
- W2126266600 countsByYear W21262666002021 @default.
- W2126266600 countsByYear W21262666002022 @default.
- W2126266600 crossrefType "journal-article" @default.
- W2126266600 hasAuthorship W2126266600A5012415802 @default.
- W2126266600 hasAuthorship W2126266600A5062305450 @default.
- W2126266600 hasBestOaLocation W21262666002 @default.
- W2126266600 hasConcept C11413529 @default.
- W2126266600 hasConcept C121332964 @default.
- W2126266600 hasConcept C158622935 @default.
- W2126266600 hasConcept C190470478 @default.
- W2126266600 hasConcept C200581526 @default.
- W2126266600 hasConcept C200741047 @default.
- W2126266600 hasConcept C202444582 @default.
- W2126266600 hasConcept C20528329 @default.
- W2126266600 hasConcept C2780990831 @default.
- W2126266600 hasConcept C2781349735 @default.
- W2126266600 hasConcept C33923547 @default.
- W2126266600 hasConcept C37914503 @default.
- W2126266600 hasConcept C55439883 @default.
- W2126266600 hasConcept C62520636 @default.
- W2126266600 hasConcept C96403706 @default.
- W2126266600 hasConceptScore W2126266600C11413529 @default.
- W2126266600 hasConceptScore W2126266600C121332964 @default.
- W2126266600 hasConceptScore W2126266600C158622935 @default.
- W2126266600 hasConceptScore W2126266600C190470478 @default.
- W2126266600 hasConceptScore W2126266600C200581526 @default.
- W2126266600 hasConceptScore W2126266600C200741047 @default.
- W2126266600 hasConceptScore W2126266600C202444582 @default.
- W2126266600 hasConceptScore W2126266600C20528329 @default.
- W2126266600 hasConceptScore W2126266600C2780990831 @default.
- W2126266600 hasConceptScore W2126266600C2781349735 @default.
- W2126266600 hasConceptScore W2126266600C33923547 @default.
- W2126266600 hasConceptScore W2126266600C37914503 @default.
- W2126266600 hasConceptScore W2126266600C55439883 @default.
- W2126266600 hasConceptScore W2126266600C62520636 @default.
- W2126266600 hasConceptScore W2126266600C96403706 @default.
- W2126266600 hasIssue "1" @default.
- W2126266600 hasLocation W21262666001 @default.
- W2126266600 hasLocation W21262666002 @default.
- W2126266600 hasOpenAccess W2126266600 @default.
- W2126266600 hasPrimaryLocation W21262666001 @default.
- W2126266600 hasRelatedWork W1988842480 @default.
- W2126266600 hasRelatedWork W1999123830 @default.
- W2126266600 hasRelatedWork W2066340280 @default.
- W2126266600 hasRelatedWork W2363992932 @default.
- W2126266600 hasRelatedWork W2407703317 @default.
- W2126266600 hasRelatedWork W2553874493 @default.
- W2126266600 hasRelatedWork W2910725637 @default.
- W2126266600 hasRelatedWork W3016485951 @default.
- W2126266600 hasRelatedWork W4298165065 @default.
- W2126266600 hasRelatedWork W4324107090 @default.
- W2126266600 hasVolume "5" @default.
- W2126266600 isParatext "false" @default.
- W2126266600 isRetracted "false" @default.
- W2126266600 magId "2126266600" @default.
- W2126266600 workType "article" @default.