On the stability of periodic trajectories of a planar Birkhoff billiard

DOI10.1134/S0081543816080125zbMath1383.37029MaRDI QIDQ521552

Anatoliy P. Markeev

Publication date: 11 April 2017

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Cites Work

• On a conjugacy problem in billiard dynamics
• Problem of stability of two-link trajectories in a multidimensional Birkhoff billiard
• A constructive method of establishing the validity of the theory of systems with non-retaining constraints
• On stability of a non-autonomous Hamiltonian system in parametric resonance of dominant mode
• On the question of the stability of the periodic trajectories of Birkhoff's billiard
• The stability of periodic trajectories of a billiard ball in three dimensions
• A method for analytically representing area-preserving mappings
• Billiard map and rigid rotation
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• On the fixed points stability for the area-preserving maps
• On the stability of the two-link trajectory of the parabolic Birkhoff billiards
• Simplifying the structure of the third and fourth degree forms in the expansion of the Hamiltonian with a linear transformation
• The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards
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