TY - JOUR
T1 - Periodic orbits for a class of reversible quadratic vector field on R3
AU - Buzzi, Claudio A.
AU - Llibre, Jaume
AU - Medrado, João C.
PY - 2007/11/15
Y1 - 2007/11/15
N2 - For a class of reversible quadratic vector fields on R3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U2. More specifically, we prove that for all n ∈ N, there exists εn > 0 such that the reversible quadratic polynomial differential system{Mathematical expression} in R3, with a0 < 0, b1 c1 < 0, a2 < 0, b2 < a2, a4 > 0, c2 < a2 and b3 ∉ {c4, 4 c4}, for ε ∈ (0, εn) has at least n periodic orbits near the heteroclinic loop. © 2007 Elsevier Inc. All rights reserved.
AB - For a class of reversible quadratic vector fields on R3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U2. More specifically, we prove that for all n ∈ N, there exists εn > 0 such that the reversible quadratic polynomial differential system{Mathematical expression} in R3, with a0 < 0, b1 c1 < 0, a2 < 0, b2 < a2, a4 > 0, c2 < a2 and b3 ∉ {c4, 4 c4}, for ε ∈ (0, εn) has at least n periodic orbits near the heteroclinic loop. © 2007 Elsevier Inc. All rights reserved.
KW - Periodic orbits
KW - Quadratic vector fields
KW - Reversibility
U2 - https://doi.org/10.1016/j.jmaa.2007.02.011
DO - https://doi.org/10.1016/j.jmaa.2007.02.011
M3 - Article
VL - 335
SP - 1335
EP - 1346
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
ER -