Bifurcation into invariant tori at points of resonance

1. Arnold, V.I., Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Functional Anal. and its Appl. Vol. 11, no. 2 (1977)

   Google Scholar 

2. Iooss, G., & D.D. Joseph, Bifurcation and stability of nT-periodic solutions branching from T-periodic solutions at points of resonance. Arch. Rational Mech. Anal. 66 (1977).

3. Lanford, O.E., Bifurcation of periodic solutions into invariant tori: the work of Ruelle and Takens, Nonlinear Problems in the Physical Sciences and Biology, Lecture Notes in Math. 322, Springer-Verlag, New York, (1973).

   Google Scholar 

4. Ruelle, D., Bifurcation in the presence of a symmetry group. Arch. Rational Mech. Anal. 51 (1973).

5. Ruelle, D, & F. Takens, On the nature of turbulence, Comm. Math. Phys. 20 (1971).

6. Sacker, R.J., On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations. New York Univ. IMM-NYU, 333, (1964).

7. Takens, F., Forced oscillations and bifurcations. Application of global analysis I, Symposium, Utrecht, State Univ. (1973).

   Google Scholar 

8. Wan, Y.H., Computation of the stability condition for the Hopf bifurcation of diffeomorphisms on ℝ². SIAM J. Appl. Math. 34, no. 1, Jan. (1978).

Download references