๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Destruction of Invariant Tori in Pendulum-Type Equations

โœ Scribed by Hai Huang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
354 KB
Volume
146
Category
Article
ISSN
0022-0396

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 potential Q=Q(t, x) # N(Q 0 ) such that the system x =Q x (t, x) does not admit any invariant torus with the rotation number (1, |).

๐Ÿ“œ SIMILAR VOLUMES

Differential Equations in Operator Algeb
Differential Equations in Operator Algebras: II. Invariance of the Order Cone
โœ Ray Redheffer; Peter Volkmann ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 340 KB

Operator differential equations such as the matrix Riccati equation u$=a+bu+ud+ucu play a prominent role in the theory of scattering and transport and in other areas of technology; see, for example, [4,5,7] and the references cited there. Especially important are conditions for invariance of the uni

Parasupersymmetry and Shape Invariance i
Parasupersymmetry and Shape Invariance in Differential Equations of Mathematical Physics and Quantum Mechanics
โœ M.A. Jafarizadeh; H. Fakhri ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 340 KB

It has been shown that all second-order associated differential equations obtained from the master function have the properties of parasupersymmetry and shape invariance. Using this fact, all of the well-known one-dimensional shape invariant parasupersymmetric Hamiltonians have been obtained by an a

Effects of a saturating dissipation in B
Effects of a saturating dissipation in Burgers-type equations
โœ A. Kurganov; P. Rosenau ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 193 KB

We propose and study a new variant of the Burgers equation with dissipation fluxes that saturate as the gradients become unbounded. If the upstream-downstream transition is above a critical threshold, the corresponding Riemann problem admits a weak solution wherein part of the transit is accomplishe