caa a22 4500 605461945 CHVBK 20210128100245.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10114-015-2456-0 doi (NATIONALLICENCE)springer-10.1007/s10114-015-2456-0 Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips [Elektronische Daten] [Tian Zhang, De Zhu] The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit. Local active coordinate system is introduced to construct the Poincaré returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the period-doubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2 n -homoclinic orbits. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Orbit flip nationallicence inclination flip nationallicence resonant nationallicence homoclinic-doubling bifurcations nationallicence Zhang Tian College of Science, University of Shanghai for Science and Technology, 200093, Shanghai, P. R. China aut Zhu De Department of Mathematics, East China Normal University, 200062, Shanghai, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1359-1366 1439-8516 31:8<1359 2015 31 10114 https://doi.org/10.1007/s10114-015-2456-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-2456-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Tian College of Science, University of Shanghai for Science and Technology, 200093, Shanghai, P. R. China aut NATIONALLICENCE 700 1- Zhu De Department of Mathematics, East China Normal University, 200062, Shanghai, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/8(2015-08-01), 1359-1366 1439-8516 31:8<1359 2015 31 10114