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 -