Mathematics Problem Archive

Showing 251-300 of 419 problems (Page 6 of 9)

AMR-050-0011
Open

Elliptic-billiard invariant k_{203,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0012
Open

Elliptic-billiard invariant k_{203,b}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0013
Open

Elliptic-billiard invariant k_{204}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0014
Open

Elliptic-billiard invariant k_{303,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0015
Open

Elliptic-billiard invariant k_{303,b}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0016
Open

Elliptic-billiard invariant k_{304}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0017
Open

Elliptic-billiard invariant k_{307}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0018
Open

Elliptic-billiard invariant k_{401}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0019
Open

Elliptic-billiard invariant k_{402}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0020
Open

Elliptic-billiard invariant k_{403,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0021
Open

Elliptic-billiard invariant k_{403,b}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0022
Open

Elliptic-billiard invariant k_{404}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0023
Open

Elliptic-billiard invariant k_{405}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0024
Open

Elliptic-billiard invariant k_{406,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0025
Open

Elliptic-billiard invariant k_{406,b}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0026
Open

Elliptic-billiard invariant k_{407}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0027
Partially Solved

Elliptic-billiard invariant k_{501}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0028
Partially Solved

Elliptic-billiard invariant k_{502}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0029
Partially Solved

Elliptic-billiard invariant k_{503}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0030
Open

Elliptic-billiard invariant k_{601}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0031
Open

Elliptic-billiard invariant k_{602}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0032
Open

Elliptic-billiard invariant k_{603}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0033
Open

Elliptic-billiard invariant k_{605,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0034
Open

Elliptic-billiard invariant k_{606}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0035
Open

Elliptic-billiard invariant k_{607}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0036
Open

Elliptic-billiard invariant k_{608}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0037
Open

Elliptic-billiard invariant k_{609}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0038
Open

Elliptic-billiard invariant k_{610}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0039
Partially Solved

Elliptic-billiard invariant k_{701}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0040
Partially Solved

Elliptic-billiard invariant k_{702}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0041
Partially Solved

Elliptic-billiard invariant k_{703}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0042
Solved

Elliptic-billiard invariant k_{802}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0043
Partially Solved

Elliptic-billiard invariant k_{803}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0044
Open

Elliptic-billiard invariant k_{804,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0045
Open

Elliptic-billiard invariant k_{804,b}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0046
Open

Elliptic-billiard invariant k_{805}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0047
Open

Elliptic-billiard invariant k_{806,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0048
Open

Elliptic-billiard invariant k_{806,b}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0049
Open

Elliptic-billiard invariant k_{807}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0050
Open

Elliptic-billiard invariant k_{808}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0051
Open

Elliptic-billiard invariant k_{809}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0052
Open

Elliptic-billiard invariant k_{810}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0053
Open

Elliptic-billiard invariant k_{811}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0054
Open

Elliptic-billiard invariant k_{812,a}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0055
Open

Elliptic-billiard invariant k_{812,b}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0056
Open

Elliptic-billiard invariant k_{813}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0057
Open

Elliptic-billiard invariant k_{814}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0058
Open

Elliptic-billiard invariant k_{815}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0059
Open

Elliptic-billiard invariant k_{816}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems
AMR-050-0060
Open

Elliptic-billiard invariant k_{817}

v1.3 research notes

Fix an ellipse with center $O$ and foci $f_1,f_2$, and let $P=(P_i)_{i=1}^N$ range over its Poncelet family of $N$-periodic billiard orbits tangent to...

L3
Dynamical Systems