Zobrazeno 1 - 10
of 157
pro vyhledávání: '"Chierchia, Luigi"'
Autor:
Argentieri, Fernando, Chierchia, Luigi
In this short note, we discuss the topology of Diophantine numbers, giving simple explicit examples of Diophantine isolated numbers (among those with same Diophantine constatnts), showing that, Diophantine sets are not always Cantor sets. General pro
Externí odkaz:
http://arxiv.org/abs/2402.00173
We review Kolmogorov's 1954 fundamental paper {\sl On the Conservation of Conditionally Periodic Motions under Small Perturbation of the Hamiltonian} (Dokl. akad. nauk SSSR,1954, vol. {\bf 98}, pp.527--530), both from the historical and the mathemati
Externí odkaz:
http://arxiv.org/abs/2402.00178
Autor:
Biasco, Luca, Chierchia, Luigi
The question of the total measure of invariant tori in analytic, nearly--integrable Hamiltonian systems is considered. In 1985, Arnol'd, Kozlov and Neishtadt, in the Encyclopaedia of Mathematical Sciences \cite{AKN1}, and in subsequent editions, conj
Externí odkaz:
http://arxiv.org/abs/2309.17041
Autor:
Biasco, Luca, Chierchia, Luigi
We introduce a new class $\mathbb{G}^n_s$ of generic real analytic potentials on $\mathbb{T}^n$ and study global analytic properties of natural nearly-integrable Hamiltonians $\frac12 |y|^2+\varepsilon f(x)$, with potential $f\in \mathbb{G}^n_s$, on
Externí odkaz:
http://arxiv.org/abs/2306.13527
Autor:
Biasco, Luca, Chierchia, Luigi
We discuss the holomorphic properties of the complex continuation of the classical Arnol'd-Liouville action-angle variables for real analytic 1 degree--of--freedom Hamiltonian systems depending on external parameters in suitable `generic standard for
Externí odkaz:
http://arxiv.org/abs/2306.00875
Autor:
Biasco, Luca, Chierchia, Luigi
In this note we present and briefly discuss results, which include as a particular case the theorem announced in [L. Biasco, and L. Chierchia. On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems. Atti Accad. Naz. Lince
Externí odkaz:
http://arxiv.org/abs/2206.01055
Autor:
Biasco, Luca, Chierchia, Luigi
We consider a 1D mechanical system $$\bar {\mathtt H}(\mathtt P,\mathtt Q)=\mathtt P^2+\bar {\mathtt G}(\mathtt Q)$$ in action-angle variable $(\mathtt P,\mathtt Q)$ where $\bar {\mathtt G}$ is a $2\pi$-periodic analytic function with non degenerate
Externí odkaz:
http://arxiv.org/abs/2003.05211
Autor:
Biasco, Luca, Chierchia, Luigi
A conjecture of Arnold, Kozlov and Neishtadt on the exponentially small measure of the non-torus set in analytic systems with two degrees of freedom is discussed.
Externí odkaz:
http://arxiv.org/abs/1912.02463
Publikováno v:
Regular and Chaotic Dynamics, Volume 24, Issue 6 of 2019
We review V.I. Arnold's 1963 celebrated paper \cite{ARV63} {\sl Proof of A.N. Kolmogorov's theorem on the conservation of conditionally periodic motions with a small variation in the Hamiltonian}, and prove that, optimizing Arnold's scheme, one can g
Externí odkaz:
http://arxiv.org/abs/1908.02523
Autor:
Biasco, Luca, Chierchia, Luigi
In [3] (Rend. Lincei Mat. Appl. 26 (2015), 1-10; see also arXiv:1503.08145 [math.DS]) the following result has been announced: Theorem. Consider a real-analytic nearly-integrable mechanical system with potential $f$, namely, a Hamiltonian system with
Externí odkaz:
http://arxiv.org/abs/1702.06480