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Rand, David A.

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Author ID: rand.david-a Recent zbMATH articles by "Rand, David A."
Published as: Rand, D.; Rand, D. A.; Rand, David; Rand, David A.
Homepage: http://www.davidrand.co.uk/index.html
External Links: MGP · Wikidata
Documents Indexed: 66 Publications since 1974, including 4 Books
Biographic References: 2 Publications

Publications by Year

Citations contained in zbMATH

46 Publications have been cited 592 times in 501 Documents Cited by Year
Universal properties of the transition from quasi-periodicity to chaos in dissipative systems. Zbl 0538.58025
Ostlund, Stellan; Rand, David; Sethna, James; Siggia, Eric
65
1983
Exotic phenomena in games and duopoly models. Zbl 0393.90014
Rand, David
65
1978
The singularity spectrum f(\(\alpha\) ) for cookie-cutters. Zbl 0664.58022
Rand, D. A.
57
1989
Correlation equations and pair approximations for spatial ecologies. Zbl 1001.92552
Rand, D. A.
41
1999
Phase portraits and bifurcations of the non-linear oscillator: \(x''+(\alpha+\gamma x^ 2)x'+\beta x+\delta x^ 3=0\). Zbl 0453.70015
Holmes, P.; Rand, D.
41
1980
Dynamics and symmetry. Predictions for modulated waves in rotating fluids. Zbl 0495.76031
Rand, David
39
1982
Bifurcations in one dimension. I. The nonwandering set. Zbl 0475.58014
Jonker, Leo; Rand, David
24
1981
The topological classification of Lorenz attractors. Zbl 0375.58015
Rand, David
21
1978
The entropy function for characteristic exponents. Zbl 0643.58006
Bohr, Tomas; Rand, David
20
1987
Bifurcations of the forced van der Pol oscillator. Zbl 0375.34031
Holmes, P. J.; Rand, D. A.
20
1978
The bifurcations of Duffing’s equation: An application of catastrophe theory. Zbl 0337.34049
Holmes, P. J.; Rand, D. A.
17
1976
The periodic orbits and entropy of certain maps of the unit interval. Zbl 0437.58017
Jonker, Leo; Rand, David
13
1980
Local adaptive Galerkin bases for large-dimensional dynamical systems. Zbl 0729.58034
Broomhead, D. S.; Indik, R.; Newell, A. C.; Rand, D. A.
12
1991
Smoothness of holonomies for codimension 1 hyperbolic dynamics. Zbl 1027.37016
Pinto, A. A.; Rand, D. A.
11
2002
Turbulent transport and the random occurrence of coherent events. Zbl 0655.76046
Newell, Alan C.; Rand, David A.; Russell, David
11
1988
Global phase space universality, smooth conjugacies and renormalisation. I: The \(C^{1+\alpha}\) case. Zbl 0697.58029
Rand, D. A.
10
1988
Fine structures of hyperbolic diffeomorphisms. Zbl 1167.37003
Pinto, Alberto A.; Rand, David A.; Ferreira, Flávio
9
2009
Bifurcations in one dimension. II. A versal model for bifurcations. Zbl 0475.58015
Jonker, Leo; Rand, David
9
1981
Universal properties of maps of the circle with \(\epsilon\)-singularities. Zbl 0545.58034
Jonker, Leo; Rand, David A.
8
1983
A mechanism for localized turbulence. Zbl 0751.76041
Bohr, T.; Rand, D. A.
7
1991
Thresholds in Pareto sets. Zbl 0357.90016
Rand, David
7
1976
Quantifying the strength of ligand antagonism in TCR triggering. Zbl 1334.92154
van den Berg, H. A.; Burroughs, N. J.; Rand, D. A.
6
2002
Spatio-temporal chaos. III: Natural spatio-temporal measures for coupled circle map lattices. Zbl 0776.58014
Gundlach, V. M.; Rand, D. A.
6
1993
Existence, non-existence and universal breakdown of dissipative golden invariant tori. I: Golden critical circle maps. Zbl 0759.58040
Rand, D. A.
6
1992
Solenoid functions for hyperbolic sets on surfaces. Zbl 1152.37013
Pinto, Alberto A.; Rand, David A.
5
2007
Cantor exchange systems and renormalization. Zbl 1126.37007
Pinto, A. A.; Rand, D. A.; Ferreira, F.
5
2007
Rigidity of hyperbolic sets on surfaces. Zbl 1173.37317
Pinto, A. A.; Rand, D. A.
5
2005
Teichmüller spaces and HR structures for hyperbolic surface dynamics. Zbl 1030.37028
Pinto, A. A.; Rand, D. A.
5
2002
Spatio-temporal chaos. I: Hyperbolicity, structural stability, spatio- temporal shadowing and symbolic dynamics. Zbl 0776.58012
Gundlach, V. M.; Rand, D. A.
5
1993
Universality and renormalisation in dynamical systems. Zbl 0651.58022
Rand, David
5
1988
Fractal bifurcation sets, renormalization strange sets and their universal invariants. Zbl 0635.58033
Rand, D. A.
5
1987
Classifying \(C^{1+}\) structures on dynamical fractals. I: The moduli space of solenoid functions for Markov maps on train tracks. Zbl 0843.57029
Pinto, A. A.; Rand, D. A.
4
1995
Spatio-temporal chaos. II: Unique Gibbs states for higher-dimensional symbolic systems. Zbl 0776.58013
Gundlach, V. M.; Rand, D. A.
4
1993
Dynamical systems and turbulence, Warwick 1980. Proceedings of a Symposium Held at the University of Warwick 1979/80. Zbl 0465.00017
Rand, D. A. (ed.); Young, L.-S. (ed.)
4
1981
Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: an application to single cell data. Zbl 06275402
Finkenstädt, Bärbel; Woodcock, Dan J.; Komorowski, Michal; Harper, Claire V.; Davis, Julian R. E.; White, Mike R. H.; Rand, David A.
3
2013
Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics. Zbl 1126.37028
Pinto, A. A.; Rand, D. A.; Ferreira, F.
3
2007
Measuring and characterizing spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies. Zbl 0868.35055
Rand, D. A.
3
1994
Classifying \(C^{1+}\) structures on dynamical fractals. II: Embedded trees. Zbl 0843.57030
Pinto, A. A.; Rand, D. A.
2
1995
Existence, non-existence and universal breakdown of dissipative golden invariant tori. III: Invariant circles for mappings of the annulus. Zbl 0759.58042
Rand, D. A.
2
1992
Renormalization of circle diffeomorphism sequences and Markov sequences. Zbl 1352.37120
Almeida, João P.; Pinto, Alberto A.; Rand, David A.
1
2014
Existence, uniqueness and ratio decomposition for Gibbs states via duality. Zbl 0986.37021
Pinto, A. A.; Rand, D. A.
1
2001
Existence, non-existence and universal breakdown of dissipative golden invariant tori. II: Convergence of renormalization for mappings of the annulus. Zbl 0759.58041
Rand, D. A.
1
1992
Global phase space universality, smooth conjugacies and renormalization. II: The \(C^{k + \alpha{}}\) case using rapid convergence of Markov families. Zbl 0760.58026
Pinto, A. A.; Rand, D. A.
1
1992
On the local stability of wave fronts defined by eikonal equations. Zbl 0429.58017
Rand, David
1
1980
Bifurcations of unimodal maps of the unit interval. Zbl 0502.58025
Jonker, Leo; Rand, David
1
1979
Non-unitary valuation subalgebras. Zbl 0289.13002
Rand, D. A.
1
1974
Renormalization of circle diffeomorphism sequences and Markov sequences. Zbl 1352.37120
Almeida, João P.; Pinto, Alberto A.; Rand, David A.
1
2014
Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: an application to single cell data. Zbl 06275402
Finkenstädt, Bärbel; Woodcock, Dan J.; Komorowski, Michal; Harper, Claire V.; Davis, Julian R. E.; White, Mike R. H.; Rand, David A.
3
2013
Fine structures of hyperbolic diffeomorphisms. Zbl 1167.37003
Pinto, Alberto A.; Rand, David A.; Ferreira, Flávio
9
2009
Solenoid functions for hyperbolic sets on surfaces. Zbl 1152.37013
Pinto, Alberto A.; Rand, David A.
5
2007
Cantor exchange systems and renormalization. Zbl 1126.37007
Pinto, A. A.; Rand, D. A.; Ferreira, F.
5
2007
Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics. Zbl 1126.37028
Pinto, A. A.; Rand, D. A.; Ferreira, F.
3
2007
Rigidity of hyperbolic sets on surfaces. Zbl 1173.37317
Pinto, A. A.; Rand, D. A.
5
2005
Smoothness of holonomies for codimension 1 hyperbolic dynamics. Zbl 1027.37016
Pinto, A. A.; Rand, D. A.
11
2002
Quantifying the strength of ligand antagonism in TCR triggering. Zbl 1334.92154
van den Berg, H. A.; Burroughs, N. J.; Rand, D. A.
6
2002
Teichmüller spaces and HR structures for hyperbolic surface dynamics. Zbl 1030.37028
Pinto, A. A.; Rand, D. A.
5
2002
Existence, uniqueness and ratio decomposition for Gibbs states via duality. Zbl 0986.37021
Pinto, A. A.; Rand, D. A.
1
2001
Correlation equations and pair approximations for spatial ecologies. Zbl 1001.92552
Rand, D. A.
41
1999
Classifying \(C^{1+}\) structures on dynamical fractals. I: The moduli space of solenoid functions for Markov maps on train tracks. Zbl 0843.57029
Pinto, A. A.; Rand, D. A.
4
1995
Classifying \(C^{1+}\) structures on dynamical fractals. II: Embedded trees. Zbl 0843.57030
Pinto, A. A.; Rand, D. A.
2
1995
Measuring and characterizing spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies. Zbl 0868.35055
Rand, D. A.
3
1994
Spatio-temporal chaos. III: Natural spatio-temporal measures for coupled circle map lattices. Zbl 0776.58014
Gundlach, V. M.; Rand, D. A.
6
1993
Spatio-temporal chaos. I: Hyperbolicity, structural stability, spatio- temporal shadowing and symbolic dynamics. Zbl 0776.58012
Gundlach, V. M.; Rand, D. A.
5
1993
Spatio-temporal chaos. II: Unique Gibbs states for higher-dimensional symbolic systems. Zbl 0776.58013
Gundlach, V. M.; Rand, D. A.
4
1993
Existence, non-existence and universal breakdown of dissipative golden invariant tori. I: Golden critical circle maps. Zbl 0759.58040
Rand, D. A.
6
1992
Existence, non-existence and universal breakdown of dissipative golden invariant tori. III: Invariant circles for mappings of the annulus. Zbl 0759.58042
Rand, D. A.
2
1992
Existence, non-existence and universal breakdown of dissipative golden invariant tori. II: Convergence of renormalization for mappings of the annulus. Zbl 0759.58041
Rand, D. A.
1
1992
Global phase space universality, smooth conjugacies and renormalization. II: The \(C^{k + \alpha{}}\) case using rapid convergence of Markov families. Zbl 0760.58026
Pinto, A. A.; Rand, D. A.
1
1992
Local adaptive Galerkin bases for large-dimensional dynamical systems. Zbl 0729.58034
Broomhead, D. S.; Indik, R.; Newell, A. C.; Rand, D. A.
12
1991
A mechanism for localized turbulence. Zbl 0751.76041
Bohr, T.; Rand, D. A.
7
1991
The singularity spectrum f(\(\alpha\) ) for cookie-cutters. Zbl 0664.58022
Rand, D. A.
57
1989
Turbulent transport and the random occurrence of coherent events. Zbl 0655.76046
Newell, Alan C.; Rand, David A.; Russell, David
11
1988
Global phase space universality, smooth conjugacies and renormalisation. I: The \(C^{1+\alpha}\) case. Zbl 0697.58029
Rand, D. A.
10
1988
Universality and renormalisation in dynamical systems. Zbl 0651.58022
Rand, David
5
1988
The entropy function for characteristic exponents. Zbl 0643.58006
Bohr, Tomas; Rand, David
20
1987
Fractal bifurcation sets, renormalization strange sets and their universal invariants. Zbl 0635.58033
Rand, D. A.
5
1987
Universal properties of the transition from quasi-periodicity to chaos in dissipative systems. Zbl 0538.58025
Ostlund, Stellan; Rand, David; Sethna, James; Siggia, Eric
65
1983
Universal properties of maps of the circle with \(\epsilon\)-singularities. Zbl 0545.58034
Jonker, Leo; Rand, David A.
8
1983
Dynamics and symmetry. Predictions for modulated waves in rotating fluids. Zbl 0495.76031
Rand, David
39
1982
Bifurcations in one dimension. I. The nonwandering set. Zbl 0475.58014
Jonker, Leo; Rand, David
24
1981
Bifurcations in one dimension. II. A versal model for bifurcations. Zbl 0475.58015
Jonker, Leo; Rand, David
9
1981
Dynamical systems and turbulence, Warwick 1980. Proceedings of a Symposium Held at the University of Warwick 1979/80. Zbl 0465.00017
Rand, D. A. (ed.); Young, L.-S. (ed.)
4
1981
Phase portraits and bifurcations of the non-linear oscillator: \(x''+(\alpha+\gamma x^ 2)x'+\beta x+\delta x^ 3=0\). Zbl 0453.70015
Holmes, P.; Rand, D.
41
1980
The periodic orbits and entropy of certain maps of the unit interval. Zbl 0437.58017
Jonker, Leo; Rand, David
13
1980
On the local stability of wave fronts defined by eikonal equations. Zbl 0429.58017
Rand, David
1
1980
Bifurcations of unimodal maps of the unit interval. Zbl 0502.58025
Jonker, Leo; Rand, David
1
1979
Exotic phenomena in games and duopoly models. Zbl 0393.90014
Rand, David
65
1978
The topological classification of Lorenz attractors. Zbl 0375.58015
Rand, David
21
1978
Bifurcations of the forced van der Pol oscillator. Zbl 0375.34031
Holmes, P. J.; Rand, D. A.
20
1978
The bifurcations of Duffing’s equation: An application of catastrophe theory. Zbl 0337.34049
Holmes, P. J.; Rand, D. A.
17
1976
Thresholds in Pareto sets. Zbl 0357.90016
Rand, David
7
1976
Non-unitary valuation subalgebras. Zbl 0289.13002
Rand, D. A.
1
1974
all top 5

Cited by 761 Authors

11 Pinto, Alberto Adrego
11 Rand, David A.
9 Holmes, Philip J.
9 Puu, Tönu
7 Barral, Julien
6 Gardini, Laura
6 Jonker, Leo B.
6 López, Juan Manuel
6 Marques, Francisco
5 Agliari, Anna
5 de la Llave, Rafael
5 Golubitsky, Martin A.
5 Llibre, Jaume
5 Stewart, Ian Nicholas
5 Tramontana, Fabio
5 Tresser, Charles
4 Barreira, Luis Manuel
4 Chen, Yushu
4 Glendinning, Paul Alexander
4 Guckenheimer, John M.
4 Jin, Zhen
4 Li, Ting
4 Ma, Junhai
4 Naimzada, Ahmad K.
4 Olsen, Luke
4 Seuret, Stéphane
4 Simpelaere, Dominique
4 Xu, Jian
3 Álvarez-Vizoso, Javier
3 Avila, Marc
3 Bauch, Chris T.
3 Bischi, Gian-Italo
3 Casdagli, Martin C.
3 Cavalli, Fausto
3 Chen, Hebai
3 Courbage, Maurice
3 Cvitanović, Predrag
3 Eames, Ken T. D.
3 Falconer, Kenneth J.
3 García Guirao, Juan Luis
3 Hofbauer, Franz
3 House, Thomas
3 Inaba, Naohiko
3 Kamiński, Brunon
3 Keeling, Matthew J.
3 Kenny, Brian G.
3 Kiss, István Z.
3 Knobloch, Edgar
3 Lamantia, Fabio
3 Lau, Kasing
3 Li, Risong
3 MacKay, Robert Sinclair
3 Molina-París, Carmen
3 Nusse, Helena Engelina
3 Peterson, Chris
3 Pikovsky, Arkady S.
3 Sharkey, Kieran J.
3 Shilnikov, Andrey L.
3 van den Berg, Hugo Antonius
3 Xiao, Jiaqing
3 Yuan, Zhihui
2 Almeida, Joao Paulo Andrade
2 Alsedà, Lluís
2 Arneodo, Alain
2 Askar, S. S.
2 Barkley, Dwight
2 Barrio, Roberto
2 Bi, Qinsheng
2 Blokh, Alexander M.
2 Broomhead, David S.
2 Bunimovich, Leonid Abramovich
2 Byatt-Smith, John G. B.
2 Byers, William
2 Calleja, Renato C.
2 Cánovas, Jose S.
2 Caraco, Thomas
2 Chang, Yingxiang
2 Chen, Xingwu
2 Chiarella, Carl
2 Chossat, Pascal
2 Chu, Tong
2 Chung, Kwok-Wai
2 Collet, Pierre
2 Crawford, John David
2 Dawes, Jonathan H. P.
2 de Melo, Welington
2 Dixon, Tony W.
2 Doutor, Paulo
2 Eckhardt, Bernd Helmut
2 Ehrenstein, Uwe
2 Elsadany, Abdelalim A.
2 Engler, Hans
2 Fan, Ai Hua
2 Feng, De-Jun
2 Ferreira, Flávio F.
2 Franceschini, Valter
2 Furth, Dave
2 Gambaudo, Jean-Marc
2 Garcia-Rubio, Raquel
2 Garcia, Ferran
...and 661 more Authors
all top 5

Cited in 133 Serials

61 Physica D
28 Communications in Mathematical Physics
27 Chaos, Solitons and Fractals
24 Journal of Statistical Physics
19 Ergodic Theory and Dynamical Systems
19 Chaos
15 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
13 Theoretical Population Biology
13 Journal of Theoretical Biology
10 Journal of Fluid Mechanics
10 Journal of Differential Equations
8 Journal of Mathematical Biology
8 Mathematical Biosciences
8 Dynamics and Stability of Systems
8 Communications in Nonlinear Science and Numerical Simulation
7 Physics of Fluids
7 Nonlinear Dynamics
6 Journal of Mathematical Analysis and Applications
6 Journal of Difference Equations and Applications
6 International Game Theory Review
5 Journal of Mathematical Physics
5 Advances in Mathematics
5 Applied Mathematics and Computation
5 Advances in Applied Mathematics
5 Applied Mathematics and Mechanics. (English Edition)
4 Physica A
4 Physics Reports
4 Proceedings of the American Mathematical Society
4 Linear Algebra and its Applications
4 Journal of Nonlinear Science
4 Complexity
4 Discrete and Continuous Dynamical Systems. Series B
3 Archive for Rational Mechanics and Analysis
3 Inventiones Mathematicae
3 Journal of Computational and Applied Mathematics
3 Journal of Mathematical Economics
3 Transactions of the American Mathematical Society
3 Journal of Economic Dynamics & Control
3 Journal de Mathématiques Pures et Appliquées. Neuvième Série
3 Annales de l’Institut Henri Poincaré. Physique Théorique
3 Discrete and Continuous Dynamical Systems
3 Dynamical Systems
2 Bulletin of the Australian Mathematical Society
2 International Journal of Theoretical Physics
2 Physics of Fluids, A
2 Journal of Economic Theory
2 Journal of Optimization Theory and Applications
2 Mathematics and Computers in Simulation
2 Monatshefte für Mathematik
2 Topology and its Applications
2 Acta Applicandae Mathematicae
2 Japan Journal of Applied Mathematics
2 Bulletin of the American Mathematical Society. New Series
2 Bulletin des Sciences Mathématiques
2 Decisions in Economics and Finance
2 Stochastics and Dynamics
2 Bulletin of the Brazilian Mathematical Society. New Series
2 Mathematical Biosciences and Engineering
2 Dynamic Games and Applications
2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 International Journal of Modern Physics B
1 Acta Mechanica
1 Advances in Applied Probability
1 Communications on Pure and Applied Mathematics
1 International Journal of Control
1 Journal d’Analyse Mathématique
1 Journal of Computational Physics
1 Journal of the Franklin Institute
1 Journal of the Mechanics and Physics of Solids
1 Letters in Mathematical Physics
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Nonlinearity
1 Physics Letters. A
1 Ukrainian Mathematical Journal
1 Wave Motion
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Bulletin of Mathematical Biology
1 Theoretical and Computational Fluid Dynamics
1 Anais da Academia Brasileira de Ciências
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Automatica
1 Duke Mathematical Journal
1 Glasgow Mathematical Journal
1 International Journal for Numerical Methods in Engineering
1 Meccanica
1 Memoirs of the American Mathematical Society
1 Proceedings of the Japan Academy. Series A
1 Quaestiones Mathematicae
1 Studies in Applied Mathematics
1 Theory and Decision
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Order
1 Probability Theory and Related Fields
1 Journal of Theoretical Probability
1 Applied Mathematics Letters
1 Economics Letters
1 The Annals of Applied Probability
1 Geometric and Functional Analysis. GAFA
1 Games and Economic Behavior
1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique
...and 33 more Serials
all top 5

Cited in 45 Fields

285 Dynamical systems and ergodic theory (37-XX)
79 Ordinary differential equations (34-XX)
70 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
61 Measure and integration (28-XX)
61 Biology and other natural sciences (92-XX)
40 Fluid mechanics (76-XX)
35 Probability theory and stochastic processes (60-XX)
26 Statistical mechanics, structure of matter (82-XX)
24 Mechanics of particles and systems (70-XX)
19 General topology (54-XX)
12 Partial differential equations (35-XX)
11 Global analysis, analysis on manifolds (58-XX)
11 Statistics (62-XX)
11 Systems theory; control (93-XX)
10 Numerical analysis (65-XX)
10 Information and communication theory, circuits (94-XX)
8 Operations research, mathematical programming (90-XX)
7 Combinatorics (05-XX)
7 Real functions (26-XX)
7 Difference and functional equations (39-XX)
7 Manifolds and cell complexes (57-XX)
6 Operator theory (47-XX)
5 Mechanics of deformable solids (74-XX)
4 Functions of a complex variable (30-XX)
4 Differential geometry (53-XX)
4 Geophysics (86-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Computer science (68-XX)
3 Optics, electromagnetic theory (78-XX)
3 Quantum theory (81-XX)
2 History and biography (01-XX)
2 Number theory (11-XX)
2 Functional analysis (46-XX)
2 Convex and discrete geometry (52-XX)
2 Classical thermodynamics, heat transfer (80-XX)
1 General and overarching topics; collections (00-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Commutative algebra (13-XX)
1 Algebraic geometry (14-XX)
1 Approximations and expansions (41-XX)
1 Abstract harmonic analysis (43-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Algebraic topology (55-XX)
1 Astronomy and astrophysics (85-XX)

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