PERTURBING TWO-DIMENSIONAL MAPS HAVING CRITICAL HOMOCLINIC ORBITS
1999 ◽
Vol 09
(06)
◽
pp. 1189-1195
◽
Keyword(s):
Discrete planar maps such as xn+1=f(xn)+μ g(xn, μ), xn∈ℝ2, n∈ℤ, μ∈ℝ, are studied under the assumption that the unperturbed map xn+1=f(xn) has a critical homoclinic orbit to a hyperbolic fixed point. We give either necessary and sufficient conditions for a bifurcation from zero to two homoclinic orbits as the small parameter μ crosses zero. These conditions are stated in terms of geometrical objects such as critical lines, stable and unstable manifolds.
Keyword(s):
2017 ◽
Vol 27
(09)
◽
pp. 1730030
◽
2017 ◽
Vol 27
(03)
◽
pp. 1730012
1998 ◽
Vol 08
(03)
◽
pp. 483-503
◽
2001 ◽
Vol 32
(3)
◽
pp. 201-209
◽
1999 ◽
Vol 129
(5)
◽
pp. 1081-1105
◽
2002 ◽
Vol 12
(12)
◽
pp. 2957-2966
◽
2012 ◽
Vol 22
(08)
◽
pp. 1250191