Нелинейные колебания, динамические системы и бифуркации векторных полей - Гукенхеймер Дж.
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Lecture Notes in Mathematics, Vol. 597. Springer-Verlag: New York,
Heidelberg, Berlin.
[183] Herman, M. R. [1983]. Sur les Courbes Invariantes par les
diffeomorphismes de I'Anneau, I, Asterisque, 103-104.
[184] Hirsch, M. W. [1976]. Differential Topology. Springer-Verlag: New
York, Heidelberg, Berlin.
[185] Hirsch, M. W., and Pugh, С. C. [1970]. Stable manifolds and
hyperbolic sets. Proc. Symp. Pure. Math., 14, 133-163.
[186] Hirsch, M. W., Pugh, С. C., and Shub, M. [1977]. Invariant
Manifolds. Springer Lectures Notes in Mathematics, Vol. 583. Springer-
Verlag: New York, Heidelberg, Berlin.
538
Литература
[187] Hirsch, М. W., and Smale, S. [1974]. Differential Equations,
Dynamical Systems and Linear Algebra. Academic Press: New York.
[188] Hockett, K., and Holmes, P. J. [1986]. Josephson s junction,
annulus maps, Birkhoff attractors, horseshoes and rotation sets. Ergodic
Theory Dyn. Syst. (in press).
[189] Hocking, J. G., and Young, G. S. [1961]. Topology. Addison-Wesley:
Reading, MA.
[190] Holmes, C., and Holmes, P. J. [1981]. Second order averaging and
bifurcations to subharmonics in Duffing's equation. J. Sound Vih., 78,
161-174.
[191] Holmes, P. J. [1977]. Bifurcations to divergence and flutter in
flow-induced oscillations: a finite-dimensional analysis. J. Sound Vib.,
53 (4), 471-503.
[192] Holmes, P. J. [1979a]. A nonlinear oscillator with a strange
attractor. Phil. Trans. Roy. Soc. A, 292, 419-448.
[193] Holmes, P. J. [1979b]. Domains of stability in a wind induced
oscillation problem. Trans. ASME. J. Appl. Mech., 46, 672-676.
[194] Holmes, P. J. (ed.) [1980a]. New Approaches to Nonlinear Problems
in Dynamics.
S.l.A.M. Publications: Philadelphia.
[195] Holmes, P. J. [1980b]. Averaging and chaotic motions in forced
oscillations. SIAM J. Appl. Math., 38, 65-80; Errata and addenda. SIAM J.
Appl. Math., 40, 167-168.
[196] Holmes, P. J. [1980c]. A strange family of three-dimensional vector
fields near a degenerate singularity. J. Diff. Eqns., 37, 382^104.
[197] Holmes, P. J. [1980d]. Unfolding a degenerate nonlinear oscillator:
a codimension two bifurcation. In Nonlinear Dynamics, R. H. G. Helleman
(ed.), pp. 473^188. New York Academy of Sciences: New York.
[198] Holmes, P. J. [1981a]. Center manifolds, normal forms and
bifurcations of vector fields with application to coupling between
periodic and steady motions. Physica, 20, 449^181.
[199] Holmes, P. J. [1981b]. Space- and time-periodic perturbations of
the sine-Gordon equation. In Dynamical Systems and Turbulence, D. A. Rand
and L.-S. Young (eds.), pp. 164-191. Springer Lecture Notes in
Mathematics, Vol. 898. Springer-Verlag: New York, Heidelberg, Berlin.
[200] Holmes, P. J. [1982a]. The dynamics of repeated impacts with a
sinusoidally vibrating table. J. Sound Vib., 84, 173-189.
[201] Holmes, P. J. [1982b]. Proof of nonintegrability for the Henon-
Heiles Hamiltonian near an exceptional integrable case. Physica, 5D, 335-
347.
[202] Holmes, P. J. [1986]. Chaotic motions in a weakly nonlinear model
for surface waves. J. Fluid Mech. (in press).
[203] Holmes, P. J., and Marsden, J. E. [1978]. Bifurcations to
divergence and flutter in flow-induced oscillations: an infinite-
dimensional analysis. Automatica, 14 (4), 367-384.
Литература
539
[204] Holmes, P. J., and Marsden, J. E. [1981]. A partial differential
equation with infinitely many periodic orbits: chaotic oscillations of a
forced beam. Arch. Ration. Mech. Anal. 76, 135-166.
[205] Holmes, P. J., and Marsden, J. E. [1982a]. Horseshoes in
perturbations of Hamiltonians with two degrees offreedom. Comm. Math.
Phys., 82, 523-544.
[206] Holmes, P. J., and Marsden, J. E. [1982b]. Melnikov's method and
Arnold diffusion for perturbations of integrable Hamiltonian systems. J.
Math. Phys., 23 (4), 669-675.
[207] Holmes, P. J., and Marsden, J.E. [1983a]. Horseshoes and Arnold
diffusion for Hamiltonian systems on Lie groups. Indiana Univ. Math. J.
32, 273-310.
[208] Holmes, P. J., Marsden, J.E., and Scheurle, J. [1986]. On averaging
and exponentially small Melnikov functions (in preparation).
[209] Holmes, P. J., and Rand, D.A. [1976]. The bifurcations of Duffings'
equation: an application of catastrophe theory. J. Sound Vib., 44 (2),
237-253.
[210] Holmes, P. J., and Rand, D.A. [1978]. Bifurcations of the forced
van der Pol oscillator. Quart. Appl. Math., 35, 495-509.
[211] Holmes, P.J., and Rand, D.A. [1980]. Phase portraits and
bifurcations of the non-linear oscillator x + (a + yx2)x + fix + Sx3 = 0.
Int. J. Nonlinear Mech., 15, 449^158.
[212] Holmes, P. J., and Whitley, D. С. [1983a]. On the attracting set
for Duffing's equation, I: Analytical methods for small force and
damping. In Partial Differential Equations and Dynamical Systems, W. E.
Fitzgibbon III (ed.), pp. 211-240. Pitman: London [1984].
[213] Holmes, P. J., and Whitley, D. C. [1983b]. On the attracting set
for Duffing's equation, II: A geometrical model for moderate force and
