Quarterly of Applied Mathematics · 1993 · 16 citations · 11 references
Natural SciencesManufacturing EngineeringMathematicsComplex SystemsDynamical SystemsProcess DynamicsChaos TheoryComplex DynamicsControl TheoryDissipative SystemsNonlinear ControlNonlinear DynamicsAttractor DynamicsAttractorsChaotic AttractorsCutting DynamicsDelay EquationsDissipative Dynamical SystemsMetric EntropyNonlinear Dynamical Systems
The attractor associated with a system of nonlinear differential-delay equations, arising from the Wu-Liu metal cutting model, is shown to have a noninteger pointwise dimension and positive metric entropy. Projections of the attractor onto a two-dimensional plane substantiate the existence of complex dynamics. The result suggests that certain regenerative chatter states may be chaotic.
11
Ergodic theory of chaos and strange attractors
Jean‐Pierre Eckmann, David Ruelle · Reviews of Modern Physics · 1985 · 4.9K citations
The dimension of chaotic attractors
J. Doyne Farmer, Edward Ott, James A. Yorke · Physica D Nonlinear Phenomena · 1983 · 1.1K citations
Chaos generated by the cutting process
Igor Grabec · Physics Letters A · 1986 · 101 citations
Engineering, Industrial Engineering, Manufacturing Engineering +11