TY - JOUR
AB - In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table Ω0 preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through Ω0.
AU - Huang, Guan
AU - Kaloshin, Vadim
ID - 8416
IS - 2
JF - Moscow Mathematical Journal
SN - 1609-4514
TI - On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables
VL - 19
ER -
TY - JOUR
AB - For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(μ120) dense as μ→0.
AU - Guardia, Marcel
AU - Kaloshin, Vadim
AU - Zhang, Jianlu
ID - 8418
IS - 2
JF - Archive for Rational Mechanics and Analysis
KW - Mechanical Engineering
KW - Mathematics (miscellaneous)
KW - Analysis
SN - 0003-9527
TI - Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem
VL - 233
ER -
TY - CONF
AB - This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In its third edition, seven tools have been applied to solve six different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, CORA/SX, HyDRA, Hylaa, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results provide one of the most complete assessments of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.
AU - Althoff, Matthias
AU - Bak, Stanley
AU - Forets, Marcelo
AU - Frehse, Goran
AU - Kochdumper, Niklas
AU - Ray, Rajarshi
AU - Schilling, Christian
AU - Schupp, Stefan
ID - 8570
T2 - EPiC Series in Computing
TI - ARCH-COMP19 Category Report: Continuous and hybrid systems with linear continuous dynamics
VL - 61
ER -
TY - JOUR
AB - We review V. I. Arnold’s 1963 celebrated paper [1] Proof of A. N. Kolmogorov’s Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold’s scheme, one can get “sharp” asymptotic quantitative conditions (as ε → 0, ε being the strength of the perturbation). All constants involved are explicitly computed.
AU - Chierchia, Luigi
AU - Koudjinan, Edmond
ID - 8693
JF - Regular and Chaotic Dynamics
TI - V. I. Arnold’s “pointwise” KAM theorem
VL - 24
ER -
TY - JOUR
AB - Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over ℚ that contains a conic defined over ℚ .
AU - Browning, Timothy D
AU - Sofos, Efthymios
ID - 170
IS - 3-4
JF - Mathematische Annalen
TI - Counting rational points on quartic del Pezzo surfaces with a rational conic
VL - 373
ER -