Applications of catastrophe theory to the physical sciences
From MaRDI portal
Publication:995012
DOI10.1016/0167-2789(81)90012-9zbMath1194.00017OpenAlexW2014816502MaRDI QIDQ995012
Publication date: 13 September 2010
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0167-2789(81)90012-9
Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Popularization of mathematics (00A09)
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Cites Work
- Group theoretic methods in bifurcation theory. With an appendix by P. Olver
- Boundary conditions and mode jumping in the buckling of a rectangular plate
- Catastrophes and partial differential equations
- On singularities of mappings of Euclidean spaces. I. Mappings of the plane into the plane
- Bifurcation analysis near a double eigenvalue of a model chemical reaction
- Post-buckling behavior of a nonlinearly hyperelastic thin rod with cross- section invariant under the dihedral group \(D_ n\)
- Semiclassical approximation of path integrals on and near caustics in terms of catastrophes
- A global genericity theorem for bifurcations in variational problems
- Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations
- Classification and unfoldings of degenerate Hopf bifurcations
- Imperfect bifurcation in the presence of symmetry
- Classification of unimodal critical points of functions
- Stability of shock waves for a single conservation law
- Contact equivalence for Lagrangian manifolds
- Catastrophe theory
- Stability of unfoldings in space and time
- Classification of bimodal critical points of functions
- Bifurcation analysis of nonlinear reaction-diffusion equations. II: Steady state solutions and comparison with numerical simulations
- Singularites \(C^\infty\) en presence de symétrie. En particulier en presence de la symétrie d'un groupe de Lie compact
- Applications of generic bifurcation. I
- Local normal forms of functions
- Bifurcational instability of an atomic lattice
- Applications of generic bifurcation. II
- The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
- Einige Bemerkungen zur Entfaltung symmetrischer Funktionen
- Singularity theory and an introduction to catastrophe theory
- Bifurcation analysis of nonlinear reaction diffusion equations I. Evolution equations and the steady state solutions
- A model equation arising from chemical reactor theory
- On the theory and application of the Hopf-Friedrich Bifurcation theory
- Towards a unified bifurcation theory
- Topological stability of smooth mappings
- A bifurcation theory for the instabilities of optimization and design
- Catastrophe theory as applied to the social and biological sciences: A critique
- Structural stability in physics. Proceedings of two international symposia on applications of catastrophe theory and topological concepts in physics, Tübingen, Fed. Rep. of Germany, May 2-6 and December 11-14, 1978
- Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
- The catastrophe controversy
- On Zeeman's equations for the nerve impulse
- Integrals of rapidly oscillating functions and singularities of projections of Lagrangian manifolds
- Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities
- A geometrical study of the elementary catastrophes
- Singularities of vector fields
- Stability of unfoldings
- Unfoldings of certain singularities of vectorfields: Generalized Hopf bifurcations
- Loss of stability and bifurcation at a double eigenvalue
- Stability of \(C^ \infty\) mappings. I: The division theorem
- Stability of \(C^ \infty\) mappings. III: Finitely determined map germs
- Stability of \(C^\infty\) mappings. II: Infinitesimal stability implies stability
- Topology and mechanics. I
- Stability of \(C^ \infty\) mappings. IV: Classification of stable germs by R-algebras
- Stability of \(C^ \infty\) mappings. V: Transversality
- On differentiable functions with isolated critical points
- The normal singularities of a submanifold
- A regularity theorem for conservation laws
- CRITICAL POINTS OF FUNCTIONS ON A MANIFOLD WITH BOUNDARY, THE SIMPLE LIE GROUPSBk,Ck, ANDF4AND SINGULARITIES OF EVOLUTES
- Stability predictions through a succession of folds
- SINGULARITIES OF FUNCTIONS ON BOUNDARIES, CORNERS, ETC.
- Catastrophe theory and equations of state: conditions for a butterfly singularity
- Morse Theory. (AM-51)
- Events in evolving three-dimensional vector fields
- A Second note on Symmetry of Singularities
- A Note on Symmetry of Singularities
- On the local stability of wave fronts defined by eikonal equations
- A splitting lemma for non-reflexive Banach spaces.
- Secondary States of Rectangular Plates
- Bifurcation and Stability of Convective Flows in a Rotating or not Rotating Spherical Shell
- Structural Stability, Catastrophe Theory, and Applied Mathematics
- A Qualitative Study of the Steady-State Solutions for a Continuous Flow Stirred Tank Chemical Reactor
- Qualitative analysis of a model for boundary effects in the Taylor problem
- Singularities of plane curves which occur as singular sections of the bifurcation sets of the cuspoid catastrophes
- Constitutive surfaces in fluid mechanics
- A singularity theory analysis of a thermal-chainbranching model for the explosion peninsula
- Dislocations in wave trains
- REMARKS ON THE STATIONARY PHASE METHOD AND COXETER NUMBERS
- NORMAL FORMS OF FUNCTIONS IN NEIGHBOURHOODS OF DEGENERATE CRITICAL POINTS
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- The bifurcations of duffing's equation: An application of catastrophe theory
- Secondary Bifurcation in Nonlinear Diffusion Reaction Equations
- On universal unfoldings of certain real functions on a Banach space
- CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS
- Wave front evolution and equivariant Morse lemma
- On Legendre transformations and elementary catastrophes
- Bifurcation phenomena in steady flows of a viscous fluid. I. Theory
- Bifurcation phenomena in steady flows of a viscous fluid II. Experiments
- On the instability of an internal gravity wave
- A buckling model for the set of umbilic catastrophes
- On Legendre transformations and umbilic catastrophes
- Focusing and twinkling: critical exponents from catastrophes in non-Gaussian random short waves
- The structure and evolution of flow fields and other vector fields
- Singularities and Plane Maps II: Sketching Catastrophes
- An Introduction to Catastrophe Theory and Its Applications
- On the null spaces of linear Fredholm operators depending on several parameters
- Determinacy in a class of germs on a reflexive Banach space
- Thom's Theorem for Banach Spaces
- Group Representation Theory and Branch Points of Nonlinear Functional Equations
- Qualitative methods in bifurcation theory
- The double cusp has five minima
- Diffractals
- A theory for imperfect bifurcation via singularity theory
- Universal unfoldings in Banach spaces: reduction and stability
- Generic multiparameter bifurcation from a manifold
- Finite-amplitude thermal convection in a spherical shell
- Oscillatory integrals, lagrange immersions and unfolding of singularities
- Singularities and Plane Maps
- Structurally Stable Systems are not Dense
- SINGULARITIES OF SMOOTH MAPPINGS
- Differentiable dynamical systems
- Buckling of a thin annular plate under uniform compression
- The Post‐Buckling Behaviour of Structures under Combined Loading
- Remarks on a paper of D. Ludwig
- ON MATRICES DEPENDING ON PARAMETERS
- LECTURES ON BIFURCATIONS IN VERSAL FAMILIES
- Vector and Tensor Theorems on Curved Surfaces
- An exact sequence in differential topology
- Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
- Umbilic points on Gaussian random surfaces
- Modelling critical behaviour in terms of catastrophe theory and fractal lattices
