2 problems

0 votes0 replies0 views
Density conjecture for periodic measures of transitive piecewise monotonic maps
Let $T\colon[0,1]\to[0,1]$ be a transitive piecewise monotonic map with positive topological entropy. Denote by $M_T^\mathrm{per}([0,1])$ the set of periodic measures and by…
Conjectureopendynamical-systems periodic-measures piecewise-monotonic-mapsarXiv posted 2 days ago
0 votes0 replies0 views
Bonatti's conjecture on periodic approximation in homoclinic classes
Bonatti's conjecture. Any ergodic measure supported on $H(p,f)$ can be approximated in the weak topology by periodic measures supported on $H(p,f)$ .
Conjectureopendynamical-systems homoclinic-classes periodic-measuresarXiv posted 2 days ago

Density conjecture for periodic measures of transitive piecewise monotonic maps