In this paper we prove that if there exists an invariant torus with the rotation number (1, |) in the pendulum-type equation x =Q 0 x (t, x) for a given potential Q 0 =Q 0 (t, x) # C (T 2 ), and | is a Liouville number, then for any neighborhood N(Q 0 ) of Q 0 in the C topology, there exists a poten
Generic Existence of Invariant Cantori in Pendulum-Type Equations
β Scribed by Hai Huang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 203 KB
- Volume
- 218
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We study the global existence, asymptotic behaviour, and global non-existence (blow-up) of solutions for the damped non-linear wave equation of Kirchho! type in the whole space: , and '0, with initial data u(x, 0)"u (x) and u R (x, 0)"u (x).
The stationary incompressible Navier-Stokes equations are discretized with a finite volume method in curvilinear co-ordinates. The arbitrarily shaped domain is mapped onto a rectangular block, resulting in a boundary-fitted grid. In order to obtain accurate discretizations of the transformed equatio
## Abstract The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let __X__ be a real Banach space and __T__ : __D__ β __X__ β 2