Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631503 | Applied Mathematics and Computation | 2011 | 9 Pages |
Abstract
So far most application of Kolmogorov–Arnold–Moser (KAM) theory has been restricted to smooth dynamical systems. In this paper, it is shown by a series of transformations that how KAM theory can be used to analyze the dynamical behavior of Duffing-type equations with impact. The analysis is carried out for the exampleequation(0.1)x¨+x2n+1=p(t),forx(t)>0,x(t)⩾0,x˙(t0+)=-x˙(t0-),ifx(t0)=0with p ∈ C5 being periodic. We prove that all solutions are bounded, and that there are infinitely many periodic and quasiperiodic solutions in this case.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Zhiguo Wang, Yiqian Wang,