Roads to turbulence in dissipative dynamical systems
Reviews of Modern PhysicsPublished 1 October 1981
Jean‐Pierre Eckmann
Citations827
SJR quartileQ1
SJR score18.08
SNIP16.63
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
Three scenarios leading to turbulence in theory and experiment are outlined. The respective mathematical theories are explained and compared.DOI:https://doi.org/10.1103/RevModPhys.53.643©1981 American Physical Society
Keywords
Computer ScienceEconomics, Econometrics and FinancePhysics and Astronomy
Journal of the Atmospheric SciencesDeterministic Nonperiodic Flow
19,337 Citations1963Edward N. Lorenz
NatureSimple mathematical models with very complicated dynamics
6,948 Citations1976Robert M. May
This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
Journal of Statistical PhysicsQuantitative universality for a class of nonlinear transformations
3,581 Citations1978Mitchell J. Feigenbaum
Lecture notes in mathematicsEquilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
2,295 Citations1975Rufus Bowen
Communications in Mathematical PhysicsIntermittent transition to turbulence in dissipative dynamical systems
2,027 Citations1980Yves Pomeau, Paul Manneville
Journal of Statistical PhysicsThe universal metric properties of nonlinear transformations
1,396 Citations1979Mitchell J. Feigenbaum
Grundlehren der mathematischen WissenschaftenLectures on Celestial Mechanics
1,321 Citations1971Carl Ludwig Siegel, Jürgen Moser
Communications in Mathematical PhysicsOccurrence of strange AxiomA attractors near quasi periodic flows onT m ,m≧3
786 Citations1978Sheldon E. Newhouse, David Ruelle +1 more
Journal of Fluid MechanicsMany routes to turbulent convection
644 Citations1980J. P. Gollub, S. Benson
Journal of Combinatorial Theory Series AOn finite limit sets for transformations on the unit interval
607 Citations1973N. Metropolis, M. L. Stein +1 more
An infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself and the structure and order of occurrence is universal for the class.
Transactions of the American Mathematical SocietyOn the existence of invariant measures for piecewise monotonic transformations
538 Citations1973A. Lasota, James A. Yorke
SIAM Journal on Applied MathematicsStable Orbits and Bifurcation of Maps of the Interval
463 Citations1978David A. Singer
Quarterly of Applied MathematicsA theory of nonlinear networks. I
455 Citations1964Robert K. Brayton, Jürgen Moser
This report describes a new approach to nonlinear RLC-networks which is based on the fact that the system of differential equations for such networks has the special form T/-x di dP(i, v) .
Communications in Mathematical PhysicsSensitive dependence to initial conditions for one dimensional maps
424 Citations1979John Guckenheimer
Russian Mathematical SurveysON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS
391 Citations1970A. D. Ventsel’, Mark Freidlin
Communications in Mathematical PhysicsThe transition to aperiodic behavior in turbulent systems
324 Citations1980Mitchell J. Feigenbaum
Physica D Nonlinear PhenomenaDifferent ways to turbulence in dissipative dynamical systems
304 Citations1980Paul Manneville, Yves Pomeau
Communications in Mathematical PhysicsUniversal properties of maps on an interval
217 Citations1980Pierre Collet, Jean‐Pierre Eckmann +1 more
Communications in Mathematical PhysicsA theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line
212 Citations1977P. Štefan
Physical Review LettersScaling for External Noise at the Onset of Chaos
208 Citations1981James P. Crutchfield, Michael Nauenberg +1 more
Physical Review LettersScaling Theory for Noisy Period-Doubling Transitions to Chaos
198 Citations1981Boris I. Shraiman, C. Eugene Wayne +1 more
Journal de Physique LettresIntermittency in Rayleigh-Bénard convection
171 Citations1980P. Bergé, M. Dubois +2 more
Journal de Physique LettresRayleigh-Bénard experiment in liquid helium ; frequency locking and the onset of turbulence
168 Citations1979J. Maurer, Albert Libchaber
Journal of Statistical PhysicsPeriod doubling bifurcations for families of maps on ℝ n
146 Citations1981Pierre Collet, Jean‐Pierre Eckmann +1 more
Journal de Physique LettresEffect of the Prandtl number on the onset of turbulence in liquid 4He
141 Citations1980J. Maurer, Albert Libchaber
Journal of Statistical PhysicsPeriod-doubling bifurcations and chaotic motion for a parametrically forced pendulum
136 Citations1981John B. McLaughlin
Mathematics of the USSR-SbornikSOURCES AND SINKS OF<i>A</i>-DIFFEOMORPHISMS OF SURFACES
135 Citations1974Romen V Plykin
Communications in Mathematical PhysicsInvariant measures for Markov maps of the interval
135 Citations1979Rufus Bowen
Le Journal de Physique ColloquesUNE EXPERIENCE DE RAYLEIGH-BENARD DE GEOMETRIE REDUITE ; MULTIPLICATION, ACCROCHAGE ET DEMULTIPLICATION DE FREQUENCES
120 Citations1980Albert Libchaber, J. Maurer
Journal of Statistical PhysicsSequences of infinite bifurcations and turbulence in a five-mode truncation of the Navier-Stokes equations
119 Citations1979Valter Franceschini, Claudio Tebaldi
Journal de Physique LettresIntermittent behaviour in the Belousov-Zhabotinsky reaction
106 Citations1981Yves Pomeau, Jean‐Claude Roux +3 more
Physics Letters ARepresentation of a strange attractor from an experimental study of chemical turbulence
93 Citations1980Jean‐Claude Roux, A. Rossi +2 more
Communications in Mathematical PhysicsApplications conservant une mesure absolument continue par rapport àdx sur [0, 1]
91 Citations1977David Ruelle
Mathematics of the USSR-IzvestiyaON SMALL RANDOM PERTURBATIONS OF SOME SMOOTH DYNAMICAL SYSTEMS
88 Citations1974Ju I Kifer
Communications in Mathematical PhysicsCharacteristic exponents and strange attractors
80 Citations1978Sidnie Dresher Feit
Communications in Mathematical PhysicsOn the existence of Feigenbaum's fixed point
78 Citations1981Massimo Campanino, Henri Epstein
Journal of Statistical PhysicsA Feigenbaum sequence of bifurcations in the Lorenz model
71 Citations1980Valter Franceschini
Physics Letters AFeigenbaum's ratios of two-dimensional area preserving maps
57 Citations1980Bernard Derrida, Yves Pomeau
Physics Letters AIntermittent behavior of the logistic system
45 Citations1981Gottfried Mayer‐Kress, Hermann Haken