The exact monotone twist map of infinite cylinders in the Birkhoff region of instability is studied. A variational method based on Aubry-Mather theory is used to discover infinitely many non-Birkhoff periodic orbits o...The exact monotone twist map of infinite cylinders in the Birkhoff region of instability is studied. A variational method based on Aubry-Mather theory is used to discover infinitely many non-Birkhoff periodic orbits of fixed rotation number sufficiently close to some irrational number for which the angular invariant circle does not exist.展开更多
In this paper,the authors systematically discuss orbit braids in M×I with regards to orbit configuration space FG(M,n),where M is a connected topological manifold of dimension at least 2 with an effective action ...In this paper,the authors systematically discuss orbit braids in M×I with regards to orbit configuration space FG(M,n),where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G.These orbit braids form a group,named orbit braid group,which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M,n),F(M/G,n)and F(M,n).They also consider the presentations of orbit braid groups in terms of orbit braids as generators by choosing M=C with typical actions of Zpand(Z_(2))^(2).展开更多
文摘The exact monotone twist map of infinite cylinders in the Birkhoff region of instability is studied. A variational method based on Aubry-Mather theory is used to discover infinitely many non-Birkhoff periodic orbits of fixed rotation number sufficiently close to some irrational number for which the angular invariant circle does not exist.
基金supported by the National Natural Science Foundation of China(No.11971112)。
文摘In this paper,the authors systematically discuss orbit braids in M×I with regards to orbit configuration space FG(M,n),where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G.These orbit braids form a group,named orbit braid group,which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M,n),F(M/G,n)and F(M,n).They also consider the presentations of orbit braid groups in terms of orbit braids as generators by choosing M=C with typical actions of Zpand(Z_(2))^(2).
