Real-Formal Orbital Rigidity for Germs of Real Analytic Vector Fields on the Real Plane
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-016-9314-y
Abstract: For n≥2$n \geqslant 2$, we consider Vnℝ$\mathcal {V}^{\mathbb {R}}_{n}$ the class of germs of real analytic vector fields on ℝ2,0̂$\left (\mathbb {R}^{2}, \widehat {0}\right )$ with zero (n−1)-jet and nonzero n-jet. We prove, for generic… read more here.
Keywords: germs real; real analytic; orbital rigidity; formal orbital ... See more keywords
Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-016-9529-3
Abstract: In this paper, we consider the perturbed KdV equation with Fourier multiplier $$\begin{aligned} u_{t} =- u_{xxx} + \big (M_{\xi }u+u^3 \big )_{x},\quad u(t,x+2\pi )=u(t,x),\quad \int _0^{2\pi }u(t,x)dx=0, \end{aligned}$$ut=-uxxx+(Mξu+u3)x,u(t,x+2π)=u(t,x),∫02πu(t,x)dx=0,with analytic data of size $$\varepsilon $$ε. We… read more here.
Keywords: real analytic; periodic solutions; perturbed kdv; quasi periodic ... See more keywords
On the embeddability of real hypersurfaces into hyperquadrics
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2018.04.001
Abstract: In this paper, we provide {\em effective} results on the non-embeddability of real-analytic hypersurfaces into a hyperquadric. We show that, for any $N >n \geq 1$, the defining functions $\varphi(z,\bar z,u)$ of all real-analytic hypersurfaces… read more here.
Keywords: embeddability real; subset mathbb; real analytic; analytic hypersurfaces ... See more keywords
A Real-Analytic Proof of the Simon-Wolff Theorem
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DOI: 10.1016/s0034-4877(20)30045-8
Abstract: We derive the Simon–Wolff localization criterion from the spectral averaging using an intuitive measure-theoretic lemma. read more here.
Keywords: simon wolff; simon; real analytic; proof simon ... See more keywords
Dirichlet series of two variables, real analytic Jacobi–Eisenstein series of matrix index, and Katok–Sarnak type result
Sign Up to like & getrecommendations! Published in 2018 at "Forum Mathematicum"
DOI: 10.1515/forum-2017-0119
Abstract: We study a real analytic Jacobi–Eisenstein series of matrix index and deduce several arithmetically interesting properties. In particular, we prove the followings: (a) Its Fourier coefficients are proportional to the average values of the Eisenstein… read more here.
Keywords: analytic jacobi; jacobi eisenstein; eisenstein series; real analytic ... See more keywords
Damping estimates for oscillatory integral operators with real-analytic phases and its applications
Sign Up to like & getrecommendations! Published in 2019 at "Forum Mathematicum"
DOI: 10.1515/forum-2019-0011
Abstract: Abstract In this paper, we investigate sharp damping estimates for a class of one-dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates for suitably damped oscillatory integral operators, we are able to give… read more here.
Keywords: real analytic; integral operators; operators real; oscillatory integral ... See more keywords