Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs

By Massimiliano Berti, Luca Biasco. 2011

81 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c276cd339bc399c221934832ef942c3a712c2fd5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Massimiliano Berti
2. Michela Procesi
3. P. Bolle
4. Berti M
5. M. E.
6. Bambusi D
7. C. Procesi
8. Livia Corsi

In Mathematical Physics

1. Massimiliano Berti
2. Michela Procesi
3. P. Bolle
4. C. Procesi
5. Livia Corsi
6. Berti M
7. M. E.
8. Bambusi D

In Statistical and Nonlinear Physics

1. Massimiliano Berti
2. P. Bolle
3. Michela Procesi
4. Livia Corsi
5. C. Procesi
6. Berti M
7. M. E.
8. Bambusi D

Citations in the corpus

• A KAM algorithm for the resonant non-linear Schrödinger equation (2012, methodology): “Use a combination of Birkhoff normal form and a KAM algorithm, see for instance [15], [1].”
• Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential (2010, methodology): “This has been recently proved in [1] for 1-dimensional PDEs satisfying the second order Melnikov nonresonance conditions of KAM theory.”
• An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds (2013, background): “The possibility to impose the non-resonance conditions through the “final solution” was yet observed in [3] (in a Lyapunov-Schmidt context) and in [2] for a KAM theorem.”
• Degenerate KAM theory for partial differential equations (2011, methodology): “We now state a simplified version of the KAM theorem in [4] sufficient for the applications of this paper.”
• KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation (2014, unknown): “This characterization of the set of parameters which fulfill all the required Melnikov non-resonance conditions (at any step of the iteration) was first observed in [6], [5] in an analytic setting.”
• A Normal Form for the Schrödinger Equation with Analytic Non-linearities (2010, methodology): “tion; already in the case of the non–resonant NLS this requires the use of the Toplitz-Lipschitz conditions developed in [7] and it will be proved in [16] following the method developed in [20]. 1 In [2] the non–resonance condition is apparently different since there is a hli at the numerator of (18)”
• KAM for Reversible Derivative Wave Equations (2012, unknown): “As in [3]-[4], the Cantor set of “good” parameters O∞ in (4.”