In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-...In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-1/3] non-hyperbolic symmetric closed characteristics.展开更多
In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is...In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is （r, R）-pinched with R/r〈 √2, then there exist at least n -k geometrically distinct P-symmetric closed ∑ characteristics on ∑, as a consequence, Z carry at least n geometrically distinct P-invariant closed characteristics.展开更多
Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R4. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a ...Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R4. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et at.展开更多
In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is ...In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on E and at least （n - 1） of them are non-hyperbolic. Here we call a compact star-shaped hypersurfaee E ∈R2 index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic （T, y） on E possesses positive mean index and whose Maslov-type index i（y, m） of its m-th iterate satisfies i（y, m） ≠-1 when n is even, and i（y, rn） ≠2{-1,0} when n is odd for all rn E N.展开更多
Let k≥2 be an integer and P be a 2n×2n symplectic orthogonal matrix satisfying P^(k)=I_(2n) and ker(P^(j)-I_(2n)=0,1≤j<k.For any compact convex hypersurface ∑■R^(2n) with n≥2 which is P-cyclic symmetric,i...Let k≥2 be an integer and P be a 2n×2n symplectic orthogonal matrix satisfying P^(k)=I_(2n) and ker(P^(j)-I_(2n)=0,1≤j<k.For any compact convex hypersurface ∑■R^(2n) with n≥2 which is P-cyclic symmetric,i.e.,x∈∑implies Px∈∑,we prove that if ∑ is(r,R)-pinched with R/r<√(2k+2)/k,then there exist at least n geometrically distince P-cyclic symmetric closed characteristics on ∑ for a broad class of matrices P.展开更多
Let∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when∑carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-res...Let∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when∑carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-resonant ellipsoids,our result is sharp.展开更多
In this paper, we construct first a new concrete example of asymmetric convex compact C 1,1-hypersurfaces in R 2n possessing precisely n closed characteristics. Then we prove multiplicity results on the closed charact...In this paper, we construct first a new concrete example of asymmetric convex compact C 1,1-hypersurfaces in R 2n possessing precisely n closed characteristics. Then we prove multiplicity results on the closed characteristics on convex compact hypersurfaces in R 2n pinched by not necessarily symmetric convex compact hypersurfaces.展开更多
文摘A survey of recent progress on the multiplicity and stability problems for closed characteristics on compact convex hypersurfaces in R^(2n) is given.
基金Partially supported by NNSF, RFDP of MOE of China
文摘In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-1/3] non-hyperbolic symmetric closed characteristics.
基金supported by China Postdoctoral Science Foundation(Grant No.2013M540512)National Natural Science Foundation of China(Grant Nos.10801078,11171341 and 11271200)Lab of Pure Mathematics and Combinatorics of Nankai University
文摘In this paper, let n ≥ 2 be an integer, P = diag（-In-k,In-k,Ik） for some integer κ∈[0, n）, and ∑∪→R^2n be a partially symmetric compact convex hypersurface, i.e., x ∈∑ implies Px∈∑. We prove that if ∑ is （r, R）-pinched with R/r〈 √2, then there exist at least n -k geometrically distinct P-symmetric closed ∑ characteristics on ∑, as a consequence, Z carry at least n geometrically distinct P-invariant closed characteristics.
基金partially supported by China Postdoctoral Science Foundation(Grant No.2013M540512)partially supported by NSFC(Grant No.11131004),MCME,LPMC of MOE of China,Nankai University and BCMIIS of Capital Normal University
文摘Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in R4. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et at.
基金supported by NSFC(Grant Nos.11671215,11131004 and 11471169,11401555,11222105 and 11431001)LPMC of MOE of China+3 种基金Anhui Provincial Natural Science Foundation(Grant No.1608085QA01)MCME,LPMC of MOE of ChinaNankai UniversityBAICIT of Capital Normal University
文摘In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface E C R2n, there exist at least n non-hyperbolic closed characteristics with even Maslov- type indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on E and at least （n - 1） of them are non-hyperbolic. Here we call a compact star-shaped hypersurfaee E ∈R2 index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic （T, y） on E possesses positive mean index and whose Maslov-type index i（y, m） of its m-th iterate satisfies i（y, m） ≠-1 when n is even, and i（y, rn） ≠2{-1,0} when n is odd for all rn E N.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771341,12022111).
文摘Let k≥2 be an integer and P be a 2n×2n symplectic orthogonal matrix satisfying P^(k)=I_(2n) and ker(P^(j)-I_(2n)=0,1≤j<k.For any compact convex hypersurface ∑■R^(2n) with n≥2 which is P-cyclic symmetric,i.e.,x∈∑implies Px∈∑,we prove that if ∑ is(r,R)-pinched with R/r<√(2k+2)/k,then there exist at least n geometrically distince P-cyclic symmetric closed characteristics on ∑ for a broad class of matrices P.
基金Hui Liu Partially supported by NSFC(No.11401555)China Postdoctoral Science Foundation No.2014T70589,CUSF(No.WK0010000037)Yiming Long Partially supported by NSFC。
文摘Let∑be a C^3 compact symmetric convex hypersurface in R^8.We prove that when∑carries exactly four geometrically distinct closed characteristics,then all of them must be symmetric.Due to the example of weakly non-resonant ellipsoids,our result is sharp.
基金Partially supported by the 973 Program of STM,Funds of EC of Jiangsuthe Natural Science Funds of Jiangsu(BK 2002023)+1 种基金the Post-doctorate Funds of Chinathe NNSF of China(10251001)Partially supported by the 973 Program of STM,NNSF,MCME,RFDP,PMC
文摘In this paper, we construct first a new concrete example of asymmetric convex compact C 1,1-hypersurfaces in R 2n possessing precisely n closed characteristics. Then we prove multiplicity results on the closed characteristics on convex compact hypersurfaces in R 2n pinched by not necessarily symmetric convex compact hypersurfaces.
