Sensitive Dependence on Initial Conditions of Strongly Nonlinear Periodic Orbits of the Forced Pendulum

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Stephen Wiggins, D.S. Mazel · Computers in Physics · 1990 · 3.9K citations

Natural Sciences, Systems Engineering, Complex Systems +11

On the Stability of the Center for Time Periodic Perturbations

V. K. Mel’nikov · Medical Entomology and Zoology · 1963 · 976 citations

Natural Sciences, Mathematics, Physics +12

Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators

Bernie D. Greenspan, Philip Holmes · SIAM Journal on Mathematical Analysis · 1984 · 81 citations

Natural Sciences, Mathematics, Differential Equations +15

Study of a class of subharmonic motions using a non-smooth temporal transformation (NSTT)

Valery N. Pilipchuk, Alexander F. Vakakis, M. A. F. Azeez · Physica D Nonlinear Phenomena · 1997 · 51 citations

Natural Sciences, Mathematics, Physics +10

The calculation of strongly non-linear systems close to vibration impact systems

Valery N. Pilipchuk · Journal of Applied Mathematics and Mechanics · 1985 · 50 citations

Engineering, Mechanical Engineering, Physics +14