The nature of the bufferness phenomenon in weakly dissipative systems

摘要

We propose it mechanism for accumulating attractors in finite-dimensional weakly dissipative systems. The essence of this mechanism is that if a Hamiltonian or a conservative system with one bind a half or more degrees of freedom is perturbed by small additional terms ensuring that it is dissipitive, then under certain conditions, the number of its attractors appearing in small neighborhoods of different elliptic equilibriums or cycles of the nonperturbed system can increase without bound as the perturbations tend to zero. We consider meaningful examples from mechanics and radio physics: models of the bouncing ball dynamics, Fermi accelerations, the linear oscillator with impacts, and the self-excited oscillator with a discrete sequence of RLC circuits in the feedback circuit.