4 papers
Remarks on Joachimsthal integral and Poritsky property
Maxim Arnold, Serge Tabachnikov
The billiard in an ellipse has an integral linear in momentum, the Joachimsthal integral. We show that the existence of such an integral characterizes conics. We extend this result…
Cross-ratio dynamics on ideal polygons
Maxim Arnold, Dmitry Fuchs, Ivan Izmestiev +1
Two ideal polygons, and , in the hyperbolic plane or in hyperbolic space are said to be -related if the cross-ratio $[p_i,p_{i+1},q_i,q_{i+1…
On Finite Gauss Transform
Maxim Arnold, Anatoly Eydelzon
We present an invariant density for the finite Gauss transformation of the unit interval and discuss some properties of this transformation.
Dynamics of Discrete Time Systems with a Hysteresis Stop Operator
Maxim Arnold, Nikita Begun, Pavel Gurevich +3
We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are…