Keyword

hyperbolicity

Description: A property of dynamical systems describing uniform expansion and contraction along distinct directions, also used for related geometric structures.

Primary topic: Mathematical Dynamics and Fractals (48%)

OpenAlex ID: keywords/hyperbolicity

An Introduction to Chaotic Dynamical Systems

1987 · Robert L. Devaney, Jean-Pierre Eckmann · Physics Today · 2,344

An introduction to chaotic dynamical systems

1990 · Acta Applicandae Mathematicae · 1,603

Invariant Manifolds

1977 · Morris W. Hirsch, Charles C. Pugh, et al. · Lecture notes in mathematics · 1,536

Persistence and Smoothness of Invariant Manifolds for Flows

1971 · Neil Fenichel · Indiana University Mathematics Journal · 1,135

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Moment closure hierarchies for kinetic theories

1996 · C. David Levermore · Journal of Statistical Physics · 921

Lagrangian coherent structures and mixing in two-dimensional turbulence

2000 · G. Haller, G. Yuan · Physica D Nonlinear Phenomena · 867

Occurrence of strange AxiomA attractors near quasi periodic flows onT m ,m≧3

1978 · S. Newhouse, D. Ruelle, et al. · Communications in Mathematical Physics · 792

One-Dimensional Dynamics

2005 · Springer eBooks · 771

Statistical Properties of Dynamical Systems with Some Hyperbolicity

1998 · Lai-Sang Young · Annals of Mathematics · 722

Hyperbolic conservation laws with stiff relaxation terms and entropy

1994 · Gui‐Qiang Chen, C. David Levermore, et al. · Communications on Pure and Applied Mathematics · 664

Geometry of the complex of curves I: Hyperbolicity

1999 · Howard A. Masur, Yair N. Minsky · Inventiones mathematicae · 662

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Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations

2001 · A. K. Kapila, R. Menikoff, et al. · Physics of Fluids · 647

Fundamental Issues in Finite Element Analyses of Localization of Deformation

1993 · R. DE BORST, L.J. SLUYS, et al. · Engineering Computations · 644

A Five-Equation Model for the Simulation of Interfaces between Compressible Fluids

2002 · Grégoire Allaire, Sébastien Clerc, et al. · Journal of Computational Physics · 623

Systems of Conservation Equations with a Convex Extension

1971 · K. O. Friedrichs, P. D. Lax · Proceedings of the National Academy of Sciences · 619

Hyperbolic Complex Spaces

1998 · Shoshichi Kobayashi · Grundlehren der mathematischen Wissenschaften · 611

The Ergodic Theory of Axiom A Flows

1975 · Rufus Bowen, David Ruelle · Springer eBooks · 585

Partial Differential Equations in Physics

1949 · Geroch, R P · Elsevier eBooks · 574

Structural stability of Lorenz attractors

1979 · John Guckenheimer, Robert F. Williams · Publications mathématiques de l IHÉS · 567

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Structural stability on two-dimensional manifolds

1962 · M.M. Peixoto · Topology · 554

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Snap-back repellers imply chaos in Rn

1978 · Frederick R Marotto · Journal of Mathematical Analysis and Applications · 546

The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms

1979 · Sheldon E. Newhouse · Publications mathématiques de l IHÉS · 533

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Diffeomorphisms with Many Periodic Points

1965 · Stephen Smale · Princeton University Press eBooks · 524

Normally Hyperbolic Invariant Manifolds in Dynamical Systems

1994 · Stephen Wiggins · Applied mathematical sciences · 513

Geometry of the complex of curves II: Hierarchical structure

2000 · H.A. Masur, Y.N. Minsky · Geometric and Functional Analysis · 488

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Works count: 5,893

Citation count: 87,350