53 citations · 284 across the 40 of their papers we have counts for
38 papers · 1 filter
Stochastic behavior along mean motion resonances in the restricted planar 3-body problem
Marcel Guardia, Vadim Kaloshin, Pau Martín +1
One of the most remarkable instability zones in the Solar system are Kirkwood gaps in the asteroid belt. In this paper we analyze instabilities in the famous Kirkwood gap in…
Computation of a separatrix map and a normally hyperbolic invariant lamination for the RP3BP
Marcel Guardia, Vadim Kaloshin, Pau Martín +1
In this paper we discuss the existence of a normally hyperbolic invariant lamination (NHIL) at the Kirkwood gap for the Restricted Planar Elliptic 3 Body Problem. This proble…
Birkhoff Conjecture for nearly centrally symmetric domains
Vadim Kaloshin, Comlan Edmond Koudjinan, Ke Zhang
In this paper we prove a perturbative version of a remarkable Bialy-Mironov (Ann.Math:389-413(196), 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symm…
Non co-preservation of the & -rational caustics along deformations of circles
V. Kaloshin, C. E. Koudjinan
For any given positive integer , we prove that every plane deformation of a circle which preserves the and -rational caustics is trivial i.e. the deformation con…
On some invariants of Birkhoff billiards under conjugacy
V. Kaloshin, C. E. Koudjinan
In the class of strictly convex smooth boundaries, each of which not having strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the "no…
Marked Length Spectral determination of analytic chaotic billiards with axial symmetries
Jacopo De Simoi, Vadim Kaloshin, Martin Leguil
We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to…
Length Spectrum Rigidity for piecewise analytic Bunimovich Billiards
Jianyu Chen, Vadim Kaloshin, Hong-Kun Zhang
In the paper, we establish Squash Rigidity Theorem - the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia. We also establish Stadium Rigidity Theore…
On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables
Guan Huang, Vadim Kaloshin
In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table preserving the integrability near the boundary have to be tan…
Marked Length Spectrum, homoclinic orbits and the geometry of open dispersing billiards
Péter Bálint, Jacopo De Simoi, Vadim Kaloshin +1
We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-esca…
Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem
Marcel Guardia Vadim Kaloshin, Jianlu Zhang
For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set in phase space independent of fixed measure, where the set of initial points w…
A locally integrable non-separable analytic geodesic flow
Livia Corsi, Vadim Kaloshin
We explicitely construct an example of an analytic metric on which is non-separable but it is locally integrable on an energy surface. The construction is based on a KAM-like…
Non-isometric domains with the same Marvizi-Melrose invariants
Lev Buhovsky, Vadim Kaloshin
For any strictly convex planar domain with a boundary one can associate an infinite sequence of spectral invariants introduced by Marvizi-Merlose…
Density of convex billiards with rational caustics
Vadim Kaloshin, Ke Zhang
We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of…
Random Iteration of Cylinder Maps and diffusive behavior away from resonances
Oriol Castejón, Marcel Guardia, Vadim Kaloshin
In this paper we propose a model of random compositions of cylinder maps, which in the simplified form is as follows: let and \[ f_{\…
Nearly circular domains which are integrable close to the boundary are ellipses
Guan Huang, Vadim Kaloshin, Alfonso Sorrentino
The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrabi…
Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
Patrick Bernard, K Kaloshin, K Zhang
We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + H1(, p, t), T n , p B n , t T = R/T be a nearly integrable system of arbitr…
On the Local Birkhoff Conjecture for Convex Billiards
Vadim Kaloshin, Alfonso Sorrentino
The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article…
On the Marked Length Spectrums of Generic Strictly Convex Billiard Tables
Guan Huang, Vadim Kaloshin, Alfonso Sorrentino
In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry-Mather periodic orbits of the induced billiard map, from the (…
Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances
Vadim Kaloshin, Jianlu Zhang, Ke Zhang
In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed w…
A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
M. Guardia, V. Kaloshin, J. Zhang
In this paper we study a so-called separatrix map introduced by Zaslaskii-Filonenko [ZF68] and studied by Treschev and Piftankin [Tre98, Tre02, Pif06, PT07]. We derive a second ord…
Random Iteration of Maps on a Cylinder and diffusive behavior
O. Castejón, V. Kaloshin
In this paper we propose a model of random compositions of cylinder maps, which in the simplified form is as follows: and \begin{eqna…
A note on micro-instability for Hamiltonian systems close to integrable
Abed Bounemoura, Vadim Kaloshin
In this note, we consider the dynamics associated to an epsilon-perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and…
Global instability in the elliptic restricted three body problem
Amadeu Delshams, Vadim Kaloshin, Abraham de la Rosa +1
The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries,…
Orbits of nearly integrable systems accumulating to KAM tori
Marcel Guardia, Vadim Kaloshin
Consider a sufficiently smooth nearly integrable Hamiltonian system of two and a half degrees of freedom in action-angle coordinates \[ H_ε(φ,I,t)=H_0(I)+εH_1(φ,I,t), φ\in T^2,\ I\…