[1]

G. H. M. van der Heijden, Bifurcation and chaos in drillstring dynamics,*Chaos, Solitons & Fractals*
**3**, 219–247 (1993).

[2]

J. D. Jansen, Nonlinear rotor dynamics as applied to oilwell drillstring vibrations,*J. Sound and Vibration*
**147**, 115–135 (1991).

[3]

W. B. Day, Asymptotic expansions in nonlinear rotordynamics,*Quart. Appl. Math.*
**44**, 779–792 (1987).

[4]

R. A. Zalik, The Jeffcott equations in nonlinear rotordynamics,*Quart. Appl. Math.*
**47**, 585–599 (1989).

[5]

Y. B. Kim, S. T. Noah, Bifurcation analysis for a modified Jeffcott rotor with bearing clearances,*Nonlinear Dynam.*
**1**, 221–241 (1990).

[6]

F. F. Ehrich, Some observations of chaotic vibration phenomena in high-speed rotordynamics,*J. Vibration and Acoustics*
**113**, 50–57 (1991).

[7]

G. Genta, C. Delprete, A. Tonoli, R. Vadori, Conditions for noncircular whirling of nonlinear isotropic rotors,*Nonlinear Dynam.*
**4**, 153–181 (1993).

[8]

S. K. Choi, S. T. Noah, Mode-locking and chaos in a Jeffcott rotor with bearing clearances,*J. Appl Mech.*
**61**, 131–138 (1994).

[9]

D. Bently, Forced subrotative speed dynamic action of rotating machinery, ASME Paper No. 74-PET-16, Petroleum Mechanical Engineering Conference, Dallas, Texas (1974).

[10]

R. F. Beatty, M. J. Hine, Improved rotor response of the updated high pressure oxygen turbo pump for the space shuttle main engine,*J. Vibration, Acoustics, Stress and Reliability in Design*
**111**, 163–169 (1989).

[11]

D. W. Childs, Rotordynamic characteristics of the HPOTP (high pressure oxygen turbopump) of the SSME (space shuttle main engine), Report FD-1-84, Turbomachinery Laboratories, Texas A & M University, 1984.

[12]

C. Kaas-Petersen, Computation, continuation, and bifurcation of torus solutions for dissipative maps and ordinary differential equations,*Physica*
**25D**, 288–306 (1987).

[13]

H. L. Swinney, Observations of order and chaos in nonlinear systems,*Physica*
**7D**, 3–15 (1983).

[14]

M. H. Jensen, P. Bak, T. Bohr, Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps,*Phys. Rev. A*
**30**, 1960–1969 (1984); Transition to chaos by interaction of resonances in dissipative systems. II. Josephson junctions, charge-density waves, and standard maps,*Phys. Rev. A*
**30**, 1970–1981 (1984).

[15]

D. G. Aronson, R. P. McGehee, I. G. Kevrekidis, R. Aris, Entrainment regions for periodically forced oscillators,*Phys. Rev. A*
**33**, 2190–2192 (1986).

[16]

R. S. MacKay, C. Tresser, Transition to topological chaos for circle maps,*Physica*
**19D**, 206–237 (1986).

[17]

J. A. Glazier, A. Libchaber, Quasi-periodicity and dynamical systems: an experimentalist's view,*IEEE Trans. Circuits and Systems*
**35**(7), 790–809 (1988); reprinted in H. Bai-Lin,*Chaos II*, World Scientific, Singapore, 1990.

[18]

D. Ruelle, F. Takens, On the nature of turbulence,*Commun. Math. Phys.*
**20**, 167–192 (1971)**23**, 343–344 (1971).

[19]

S. E. Newhouse, D. Ruelle, F. Takens, Occurrence of strange Axiom A attractors near quasi periodic flows on*T*
^{m},*m* ≤ 3,*Commun. Math. Phys.*
**64**, 35–40 (1978).

[20]

P. S. Linsay, A. W. Gumming, Three-frequency quasiperiodicity, phase locking, and the onset of chaos,*Physica*
**40D**, 196–217 (1989).

[21]

C. Baesens, J. Guckenheimer, S. Kim, R. S. MacKay, Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos,*Physica*
**49D**, 387–475 (1991).

[22]

H. W. Broer, C. Simó, J. C. Tatjer, Towards global models near homoclinic tangencies of dissipative diffeomorphisms, Preprint University of Groningen, The Netherlands (1993).

[23]

V. I. Arnol;d, Small denominators, I. Mappings of the circumference onto itself,*Transl. Amer. Math. Soc., Ser.*
**246**, 213–284 (1965).

[24]

E. J. Doedel, J. P. Kernevez, AUTO: Software for continuation and bifurcation problems in ordinary differential equations, Applied Mathematics Report, California Institute of Technology, 1986.

[25]

B. L. J. Braaksma, H. W. Broer, G. B. Huitema, Toward a quasi-periodic bifurcation theory,*Mem. AMS*
**83**(421), 83–175 (1990).

[26]

W. Szemplinska-Stupnicka,*The Behaviour of Nonlinear Vibrating Systems*, Vol. I and II, Kluwer Academic Publishers, Dordrecht, 1990.

[27]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling,*Numerical Recipes. The Art of Scientific Computing*, Cambridge University Press, Cambridge, 1986.

[28]

G. R. Qin, D. C. Gong, R. Li, X. D. Wen, Rich bifurcation behaviors of the driven Van der Pol oscillator,*Phys. Lett. A*
**141**, 412–416 (1989).

[29]

G. R. Qin, R. Li, D. C. Gong, L. Jiang, Equal periodic bifurcation in a real dissipative system,*Phys. Lett. A*
**137**, 255–258 (1989).

[30]

L. Glass, R. Ferez, Fine structure of phase locking,*Phys. Rev. Lett.*
**48**, 1772–1775 (1982).

[31]

D. G. Aronson, M. A. Chory, G. R. Hall, R. P. McGehee, Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study,*Commun. Math. Phys.*
**83**, 303–354 (1982).

[32]

D. L. Gonzalez, O. Piro, Chaos in a nonlinear driven oscillator with exact solution,*Phys. Rev. Lett.*
**50**, 870–872 (1983).

[33]

J. A. Sanders, F. Verhulst,*Averaging Methods in Nonlinear Dynamical Systems*, Springer-Verlag, New York, 1985.

[34]

J. Guckenheimer, P. Holmes,*Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields*, Springer, New York, 1983.

[35]

F. Verhulst, Discrete symmetric dynamical systems at the main resonances with applications to axi-symmetric galaxies,*Phil. Trans. Roy. Soc. London Ser. A*
**290**, 435–465 (1979).

[36]

S. Wiggins,*Global Bifurcations and Chaos*, Springer-Verlag, New York, 1988.