Professor Philip Holmes

It is with great pleasure that we dedicate this special issue of the ASME Journal of Computational and Nonlinear Dynamics to Professor Philip John Holmes (born in Lincolnshire, United Kingdom on May 24, 1945), in honor of his 60th birthday and his extensive contributions to the advancement of knowledge. His seminal works in dynamical-systems theory and nonlinear science are well known, and the reach of his efforts across many fields of application continues to inspire his peers and those that follow in his footsteps.

A glance at the early period of Phil’s career reveals the hallmarks of his later work: wonderful writing, clear mathematical exposition, timely significant results, and extensive fostering of collaborations across disciplinary boundaries. Together with his skills as a lecturer, his ability to instill enthusiasm and appreciation for the application of dynamical systems theory to...

1.
Holmes
,
P. J.
, and
White
,
R. G.
, 1972, “
Data Analysis Criteria and Instrumentation Requirements for the Transient Measurement of Mechanical Impedance
,”
J. Sound Vib.
0022-460X,
25
(
2
), pp.
217
243
.
2.
Holmes
,
P. J.
, 1974, “
On the Practical Estimation of Spectra and Correlation Functions of Transient Signals
,”
J. Sound Vib.
0022-460X,
32
(
4
), pp.
525
529
.
3.
Holmes
,
P. J.
, 1974, “
The Experimental Characterization of Wave Propagation Systems: I. Non-dispersive Waves in Lumped Systems
,”
J. Sound Vib.
0022-460X,
35
(
2
), pp.
253
275
.
4.
Holmes
,
P. J.
, 1974, “
The Experimental Characterization of Wave Propagation Systems: II. Continuous Systems and the Effects of Dispersion
,”
J. Sound Vib.
0022-460X,
35
(
2
), pp.
277
297
.
5.
Holmes
,
P. J.
, and
Mercer
,
C. A.
, 1976, “
Comments on Measurement of Frequency Response and the Multiple Coherence Function of the Noise Generation System of a Diesel Engine
,”
J. Acoust. Soc. Am.
0001-4966,
60
(
4
), pp.
951
952
[
Holmes
,
P. J.
, and
Mercer
,
C. A.
,1975,
J. Acoust. Soc. Am.
0001-4966,
58
(
3
), pp.
635
642
].
6.
Holmes
,
P. J.
, and
Rand
,
D. A.
, 1976, “
The Bifurcations of Duffing’s Equation: An Application of Catastrophe Theory
,”
J. Sound Vib.
0022-460X,
44
(
2
), pp.
237
253
.
7.
Holmes
,
P.
, 1977, “
Strange Phenomena in Dynamical Systems and Their Physical Implications
,”
Appl. Math. Model.
0307-904X,
1
(
7
), pp.
362
366
.
8.
Holmes
,
P. J.
, 1977, “
Bifurcations to Divergence and Flutter in Flow-Induced Oscillations: A Finite Dimensional Analysis
,”
J. Sound Vib.
0022-460X,
53
(
4
), pp.
471
503
.
9.
Holmes
,
P. J.
, 1977, “
Behavior of an Oscillator With Even Non-linear Damping
,”
Int. J. Non-Linear Mech.
0020-7462,
12
(
5
), pp.
323
326
.
10.
Holmes
,
P. J.
, and
Rand
,
D. A.
, 1978, “
Bifurcations of the Forced van der Pol Oscillator
,”
Q. Appl. Math.
0033-569X,
35
(
4
), pp.
495
509
.
11.
Holmes
,
P.
, and
Marsden
,
J.
, 1978, “
Bifurcation to Divergence and Flutter in Flow-Induced Oscillations: An Infinite Dimensional Analysis
,”
Automatica
0005-1098,
14
(
4
), pp.
367
384
.
12.
Holmes
,
P. J.
, and
Lin
,
Y. K.
, 1978, “
Deterministic Stability Analysis of a Wind-Loaded Structure
,”
ASME J. Appl. Mech.
0021-8936,
45
(
1
), pp.
165
169
.
13.
Lin
,
Y. K.
, and
Holmes
,
P. J.
, 1978, “
Stochastic Analysis of Wind-Loaded Structures
,”
J. Engrg. Mech. Div.
0044-7951,
104
(
2
), pp.
421
440
.
14.
Holmes
,
P.
, 1979, “
A Nonlinear Oscillator With a Strange Attractor
,”
Philos. Trans. R. Soc. London
0962-8428,
292
(
1394
), pp.
419
448
.
15.
Holmes
,
P. J.
, 1979, “
Pipes Supported at Both Ends Cannot Flutter
,”
ASME J. Appl. Mech.
0021-8936,
45
(
3
), pp.
619
622
.
16.
Holmes
,
P. J.
, 1979, “
Domains of Stability in a Wind-Induced Oscillation Problem
,”
ASME J. Appl. Mech.
0021-8936,
46
(
3
), pp.
672
676
.
17.
Moon
,
F. C.
, and
Holmes
,
P. J.
, 1979, “
A Magnetoelastic Strange Attractor
,”
J. Sound Vib.
0022-460X,
65
(
2
), pp.
275
296
(Addendum:
Holmes
,
P. J.
, and
Moon
,
F. C.
, 1980,
J. Sound Vib.
0022-460X,
69
(
2
), p.
339
).
18.
Holmes
,
P.
, 1980, “
Periodic, Nonperiodic and Irregular Motions in a Hamiltonian System
,”
Rocky Mt. J. Math.
0035-7596,
10
(
4
), pp.
679
693
.
19.
Rand
,
R. H.
, and
Holmes
,
P. J.
, 1980, “
Bifurcation of Periodic Motions in Two Weakly Coupled van der Pol Oscillators
,”
Int. J. Non-Linear Mech.
0020-7462,
15
(
4-5
), pp.
387
399
.
20.
Holmes
,
P.
, and
Rand
,
D.
, 1980, “
Phase Portraits and Bifurcations of the Non-linear Oscillator: ẍ +(α+γ x2 )ẋ +βx+δ x3 =0
,”
Int. J. Non-Linear Mech.
0020-7462,
15
(
6
), pp.
449
458
.
21.
Holmes
,
P. J.
, 1980, “
A Strange Family of Three-Dimensional Vector Fields Near a Degenerate Singularity
,”
J. Differ. Equations
0022-0396,
37
(
3
), pp.
382
403
.
22.
Chillingworth
,
D. R. J.
, and
Holmes
,
P. J.
, 1980, “
Dynamical Systems and Models for Reversals of the Earth’s Magnetic Field
,”
Math. Geol.
0882-8121,
12
(
1
), pp.
41
59
.
23.
Holmes
,
P. J.
, 1980, “
Averaging and Chaotic Motions in Forced Oscillations
,”
SIAM J. Appl. Math.
0036-1399,
38
(
1
), pp.
65
80
(Erratum and Addenda:
Holmes
,
P. J.
, 1981,
SIAM J. Appl. Math.
0036-1399,
40
(
1
), pp.
167
168
).
24.
Holmes
,
P.
, and
Lewis
,
D.
, 1981, “
A Periodically Forced Scalar Ordinary Differential Equation
,”
Int. J. Non-Linear Mech.
0020-7462,
16
(
3-4
), pp.
233
246
.
25.
Holmes
,
C.
, and
Holmes
,
P.
, 1981, “
Second-Order Averaging and Bifurcations to Subharmonics in Duffing’s Equation
,”
J. Sound Vib.
0022-460X,
78
(
2
), pp.
161
174
.
26.
Holmes
,
P.
, and
Marsden
,
J.
, 1981, “
A Partial Differential Equation With Infinitely Many Periodic Orbits: Chaotic Oscillations of a Forced Beam
,”
Arch. Ration. Mech. Anal.
0003-9527,
76
(
2
), pp.
135
165
.
27.
Leibovich
,
S.
, and
Holmes
,
P.
, 1981, “
Global Stability of the Burgers Vortex
,”
Phys. Fluids
0031-9171,
24
(
3
), pp.
548
549
.
28.
Holmes
,
P. J.
, 1981, “
Center Manifolds, Normal Forms and Bifurcations of Vector Fields With Application to Coupling Between Periodic and Steady Motions
,”
Physica D
0167-2789,
2
(
3
), pp.
449
481
.
29.
Holmes
,
P.
, 1982, “
Proof of Non-integrability for the Hénon-Heiles Hamiltonian Near an Exceptional Integrable Case
,”
Physica D
0167-2789,
5
(
2-3
), pp.
335
347
.
30.
Holmes
,
P.
, and
Stewart
,
D. S.
, 1982, “
The Existence of One-Dimensional Steady Detonation Waves in a Simple Model Problem
,”
Stud. Appl. Math.
0022-2526,
66
(
2
), pp.
121
143
.
31.
Holmes
,
P.
, 1982, “
On a Second-Order Boundary Value Problem Arising in Combustion Theory
,”
Q. Appl. Math.
0033-569X,
40
(
1
), pp.
53
62
.
32.
Holmes
,
P. J.
, 1982, “
The Dynamics of Repeated Impacts With a Sinusoidally Vibrating Table
,”
J. Sound Vib.
0022-460X,
84
(
2
), pp.
173
189
(Erratum:
Holmes
,
P. J.
, 1983,
J. Sound Vib.
0022-460X,
88
(
2
), pp.
287
288
).
33.
Holmes
,
P. J.
, and
Marsden
,
J. E.
, 1982, “
Melnikov’s Method and Arnold Diffusion for Perturbations of Integrable Hamiltonian Systems
,”
J. Math. Phys.
0022-2488,
23
(
4
), pp.
669
675
.
34.
Cohen
,
A. H.
,
Holmes
,
P. J.
, and
Rand
,
R. H.
, 1982, “
The Nature of the Coupling Between Segmental Oscillators of the Lamprey Spinal Generator for Locomotion: A Mathematical Model
,”
J. Math. Biol.
0303-6812,
13
(
3
), pp.
345
369
.
35.
Holmes
,
P. J.
, and
Marsden
,
J. E.
, 1982, “
Horseshoes in Perturbations of Hamiltonian Systems With Two Degrees of Freedom
,”
Commun. Math. Phys.
0010-3616,
82
(
4
), pp.
523
544
.
36.
Holmes
,
P.
, and
Whitley
,
D.
, 1983, “
On the Attracting Set for Duffing’s Equation. II. A Geometrical Model for Moderate Force and Damping
,”
Physica D
0167-2789,
7
(
1-3
), pp.
111
123
.
37.
Shaw
,
S. W.
, and
Holmes
,
P.
, 1983, “
Periodically Forced Linear Oscillator With Impacts: Chaos and Long Period Motions
,”
Phys. Rev. Lett.
0031-9007,
51
(
8
), pp.
623
626
.
38.
Holmes
,
P. J.
, and
Moon
,
F. C.
, 1983, “
Strange Attractors and Chaos in Nonlinear Mechanics
,”
ASME J. Appl. Mech.
0021-8936,
50
(
4B
), pp.
1021
1032
.
39.
Shaw
,
S. W.
, and
Holmes
,
P. J.
, 1983, “
A Periodically Forced Impact Oscillator With Large Dissipation
,”
ASME J. Appl. Mech.
0021-8936,
50
(
4A
), pp.
849
857
.
40.
Shaw
,
S. W.
, and
Holmes
,
P. J.
, 1983, “
A Periodically Forced Piecewise Linear Oscillator
,”
J. Sound Vib.
0022-460X,
90
(
1
), pp.
129
155
.
41.
Holmes
,
P. J.
, and
Marsden
,
J. E.
, 1983, “
Horseshoes and Arnold Diffusion for Hamiltonian Systems on Lie Groups
,”
Indiana Univ. Math. J.
0022-2518,
32
(
2
), pp.
273
309
.
42.
Moroz
,
I. M.
, and
Holmes
,
P.
, 1984, “
Double Hopf Bifurcation and Quasi-Periodic Flow in a Model for Baroclinic Instability
,”
J. Atmos. Sci.
0022-4928,
41
(
21
), pp.
3147
3160
.
43.
Holmes
,
P.
, and
Spence
,
D.
, 1984, “
On a Painlevé-type Boundary Value Problem
,”
Q. J. Mech. Appl. Math.
0033-5614,
37
(
4
), pp.
525
538
.
44.
Holmes
,
P.
, and
Whitley
,
D.
, 1984, “
Bifurcations of One- and Two-Dimensional Maps
,”
Philos. Trans. R. Soc. London
0962-8428,
311
(
1515
), pp.
43
102
(Erratum:
Holmes
,
P.
, 1984,
Philos. Trans. R. Soc. London
0962-8428,
312
(
1523
), pp.
601
).
45.
Holmes
,
P.
, 1984, “
Bifurcation Sequences in Horseshoe Maps: Infinitely Many Routes to Chaos
,”
Phys. Lett.
0370-2693,
104A
(
6-7
), pp.
299
302
.
46.
Belair
,
J.
, and
Holmes
,
P.
, 1984, “
On Linearly Coupled Relaxation Oscillations
,”
Q. Appl. Math.
0033-569X,
42
(
2
), pp.
193
219
.
47.
Greenspan
,
B.
, and
Holmes
,
P.
, 1984, “
Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators
,”
SIAM J. Math. Anal.
0036-1410,
15
(
1
), pp.
69
97
.
48.
Holmes
,
P.
, and
Williams
,
R. F.
, 1985, “
Knotted Periodic Orbits in Suspensions of Smale’s Horseshoe: Torus Knots and Bifurcation Sequences
,”
Arch. Ration. Mech. Anal.
0003-9527,
90
(
2
), pp.
115
194
.
49.
Holmes
,
P.
, 1985, “
Dynamics of a Nonlinear Oscillator With Feedback Control. I. Local Analysis
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
107
(
2
), pp.
159
165
.
50.
Veerman
,
P.
, and
Holmes
,
P.
, 1985, “
The Existence of Arbitrarily Many Distinct Periodic Orbits in a Two Degree of Freedom Hamiltonian System
,”
Physica D
0167-2789,
14
(
2
), pp.
177
192
.
51.
Holmes
,
P.
, 1986, “
Spatial Structure of Time-Periodic Solutions of the Ginzburg-Landau Equation
,”
Physica D
0167-2789,
23
(
1-3
), pp.
84
90
.
52.
Hockett
,
K.
, and
Holmes
,
P.
, 1986, “
Josephson’s Junction, Annulus Maps, Birkhoff Attractors, Horseshoes and Rotation Sets
,”
Ergod. Theory Dyn. Syst.
0143-3857,
6
(
2
), pp.
205
239
.
53.
Holmes
,
P.
, 1986, “
Knotted Periodic Orbits in Suspensions of Smale’s Horseshoe: Period Multiplying and Cabled Knots
,”
Physica D
0167-2789,
21
(
1
), pp.
7
41
.
54.
Veerman
,
P.
, and
Holmes
,
P.
, 1986, “
Resonance Bands in a Two Degree of Freedom Hamiltonian System
,”
Physica D
0167-2789,
20
(
2-3
), pp.
413
422
.
55.
Holmes
,
P.
, 1986, “
Chaotic Motions in a Weakly Nonlinear Model for Surface Waves
,”
J. Fluid Mech.
0022-1120,
162
, pp.
365
388
.
56.
Kiemel
,
T.
, and
Holmes
,
P.
, 1987, “
A Model for the Periodic Synaptic Inhibition of a Neuronal Oscillator
,”
IMA J. Math. Appl. Med. Biol.
0265-0746,
4
(
2
), pp.
145
169
.
57.
Hockett
,
K.
, and
Holmes
,
P.
, 1987, “
Nonlinear Oscillators, Iterated Maps, Symbolic Dynamics and Knotted Orbits
,”
Proc. IEEE
0018-9219,
75
(
8
), pp.
1071
1080
.
58.
Wiggins
,
S.
, and
Holmes
,
P.
, 1987, “
Periodic Orbits in Slowly Varying Oscillators
,”
SIAM J. Math. Anal.
0036-1410,
18
(
3
), pp.
592
611
.
59.
Wiggins
,
S.
, and
Holmes
,
P.
, 1987, “
Homoclinic Orbits in Slowly Varying Oscillators
,”
SIAM J. Math. Anal.
0036-1410,
18
(
3
), pp.
612
629
(Erratum:
Wiggins
,
S.
, and
Holmes
,
P.
, 1988,
SIAM J. Math. Anal.
0036-1410,
19
(
5
), pp.
1254
1255
).
60.
Brunsden
,
V.
, and
Holmes
,
P.
, 1987, “
Power Spectra of Strange Attractors Near Homoclinic Orbits
,”
Phys. Rev. Lett.
0031-9007,
58
(
17
), pp.
1699
1702
.
61.
Holmes
,
P. J.
, 1987, “
Knotted Periodic Orbits in Suspensions of Annulus Maps
,”
Proc. R. Soc. London, Ser. A
1364-5021,
411
(
1841
), pp.
351
378
.
62.
Moon
,
F. C.
,
Cusumano
,
J.
, and
Holmes
,
P. J.
, 1987, “
Evidence for Homoclinic Orbits as a Precursor to Chaos in a Magnetic Pendulum
,”
Physica D
0167-2789,
24
(
1-3
), pp.
383
390
.
63.
Holmes
,
P.
,
Marsden
,
J.
, and
Scheurle
,
J.
, 1988, “
Exponentially Small Splittings of Separatrices With Applications to KAM Theory and Degenerate Bifurcations
,”
Contemp. Math.
0271-4132,
81
, pp.
213
244
.
64.
Hockett
,
K.
, and
Holmes
,
P.
, 1988, “
Bifurcation to Rotating Cantor Sets in Maps of the Circle
,”
Nonlinearity
0951-7715,
1
(
4
), pp.
603
616
.
65.
Szeri
,
A.
, and
Holmes
,
P.
, 1988, “
Nonlinear Stability of Axisymmetric Swirling Flows
,”
Philos. Trans. R. Soc. London
0962-8428,
326
(
1590
), pp.
327
354
(Erratum:
Szeri
,
A.
, 1988,
Philos. Trans. R. Soc. London
0962-8428,
326
(
1593
), p.
697
).
66.
Aubry
,
N.
,
Holmes
,
P.
,
Lumley
,
J. L.
, and
Stone
,
E.
, 1988, “
The Dynamics of Coherent Structures in the Wall Region of a Turbulent Boundary Layer
,”
J. Fluid Mech.
0022-1120,
192
, pp.
115
173
(Corrigendum:
Aubry
,
N.
,
Holmes
,
P.
,
Lumley
,
J. L.
, and
Stone
,
E.
, 1996,
J. Fluid Mech.
0022-1120,
324
, pp.
407
408
).
67.
Mielke
,
A.
, and
Holmes
,
P.
, 1988, “
Spatially Complex Equilibria of Buckled Rods
,”
Arch. Ration. Mech. Anal.
0003-9527,
101
(
4
), pp.
319
348
.
68.
Hockett
,
K.
, and
Holmes
,
P.
, 1988, “
Bifurcation to Badly Ordered Orbits in One-Parameter Families of Circle Maps, or Angels Fallen From the Devil’s Staircase
,”
Proc. Am. Math. Soc.
0002-9939,
102
(
4
), pp.
1031
1051
.
69.
Armbruster
,
D.
,
Guckenheimer
,
J.
, and
Holmes
,
P.
, 1988, “
Heteroclinic Cycles and Modulated Travelling Waves in Systems With O(2) Symmetry
,”
Physica D
0167-2789,
29
(
3
), pp.
257
282
.
70.
Guckenheimer
,
J.
, and
Holmes
,
P.
, 1988, “
Structurally Stable Heteroclinic Cycles
,”
Math. Proc. Cambridge Philos. Soc.
0305-0041,
103
(
1
), pp.
189
192
.
71.
Holmes
,
P.
, 1989, “
Knotted Periodic Orbits in Suspensions of Smale’s Horseshoe: Extended Families and Bifurcation Sequences
,”
Physica D
0167-2789,
40
(
1
), pp.
42
64
.
72.
Aubry
,
N.
,
Holmes
,
P.
,
Lumley
,
J. L.
, and
Stone
,
E.
, 1989, “
Application of Dynamical Systems Theory to Coherent Structures in the Wall Region
,”
Physica D
0167-2789,
37
(
1-3
), pp.
1
10
(Erratum:
Aubry
,
N.
,
Holmes
,
P.
,
Lumley
,
J. L.
, and
Stone
,
E.
, 1997,
Physica D
0167-2789,
104
(
2
), pp.
212
213
).
73.
Stone
,
E.
, and
Holmes
,
P.
, 1989, “
Noise Induced Intermittency in a Model of a Turbulent Boundary Layer
,”
Physica D
0167-2789,
37
(
1-3
), pp.
20
32
(Erratum:
Aubry
,
N.
,
Holmes
,
P.
,
Lumley
,
J. L.
, and
Stone
,
E.
, 1997,
Physica D
0167-2789,
104
(
2
), pp.
212
213
).
74.
Armbruster
,
D.
,
Guckenheimer
,
J.
, and
Holmes
,
P.
, 1989, “
Kuramoto-Sivashinsky Dynamics on the Center-Unstable Manifold
,”
SIAM J. Appl. Math.
0036-1399,
49
(
3
), pp.
676
691
.
75.
Brunsden
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, 1997, “
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, 1998, “
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Euler Buckling in a Potential Field
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Homoclinic Orbits and Chaos in Three- and Four-Dimensional Flows
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, and
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, 2002, “
Mechanisms Underlying Dependencies of Performance on Stimulus Histories in a Two-Alternative Forced-Choice Task
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Ninety Plus Thirty Years of Nonlinear Dynamics: Less is More and More is Different
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The Dynamics of Legged Locomotion: Models, Analyses, and Challenges
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