?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Facta.bibl.u-szeged.hu%2F76536%2F&rft.title=On+the+cyclicity+of+Kolmogorov+polycycles&rft.creator=+Mar%C3%ADn+David&rft.creator=+Villadelprat+Jordi&rft.subject=01.+Term%C3%A9szettudom%C3%A1nyok&rft.subject=01.01.+Matematika&rft.description=In+this+paper+we+study+planar+polynomial+Kolmogorov%E2%80%99s+differential+systems+X%C2%B5+x%CB%99+%3D+x+f(x%2C+y%3B+%C2%B5)%2C+y%CB%99+%3D+yg(x%2C+y%3B+%C2%B5)%2C+with+the+parameter+%C2%B5+varying+in+an+open+subset+%CE%9B+%E2%8A%82+RN.+Compactifying+X%C2%B5+to+the+Poincar%C3%A9+disc%2C+the+boundary+of+the+first+quadrant+is+an+invariant+triangle+%CE%93%2C+that+we+assume+to+be+a+hyperbolic+polycycle+with+exactly+three+saddle+points+at+its+vertices+for+all+%C2%B5+%E2%88%88+%CE%9B.+We+are+interested+in+the+cyclicity+of+%CE%93+inside+the+family+%7BX%C2%B5%7D%C2%B5%E2%88%88%CE%9B%2C+i.e.%2C+the+number+of+limit+cycles+that+bifurcate+from+%CE%93+as+we+perturb+%C2%B5.+In+our+main+result+we+define+three+functions+that+play+the+same+role+for+the+cyclicity+of+the+polycycle+as+the+first+three+Lyapunov+quantities+for+the+cyclicity+of+a+focus.+As+an+application+we+study+two+cubic+Kolmogorov+families%2C+with+N+%3D+3+and+N+%3D+5%2C+and+in+both+cases+we+are+able+to+determine+the+cyclicity+of+the+polycycle+for+all+%C2%B5+%E2%88%88+%CE%9B%2C+including+those+parameters+for+which+the+return+map+along+%CE%93+is+the+identity.&rft.date=2022&rft.type=Foly%C3%B3irat&rft.type=NonPeerReviewed&rft.format=full&rft.language=hu&rft.identifier=http%3A%2F%2Facta.bibl.u-szeged.hu%2F76536%2F1%2Fejqtde_2022_035.pdf&rft.identifier=+++Mar%C3%ADn+David%3B++Villadelprat+Jordi%3A+++On+the+cyclicity+of+Kolmogorov+polycycles.++(2022)+++&rft.language=eng