Rigorous computational shadowing of orbits of ordinary differential equations

Deterministic Nonperiodic Flow

Edward N. Lorenz · Journal of the Atmospheric Sciences · 1963 · 19.3K citations · Full text

Natural Sciences, Mathematics, Physics +12

The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors.

John Guckenheimer, Colin Sparrow · American Mathematical Monthly · 1984 · 1.2K citations

Natural Sciences, Mathematics, Physics +17

ω-Limit sets for Axiom A diffeomorphisms

Rufus Bowen · Journal of Differential Equations · 1975 · 305 citations

Natural Sciences, Mathematics, Physics +10

Do numerical orbits of chaotic dynamical processes represent true orbits?

Stephen Hammel, James A. Yorke, Celso Grebogi · Journal of Complexity · 1987 · 249 citations

Natural Sciences, Mathematics, Physics +14

Hyperbolicity and chain recurrence

John E. Franke, James F. Selgrade · Journal of Differential Equations · 1977 · 83 citations

Natural Sciences, Mathematics, Dynamical Systems +8