TAILIEUCHUNG - Đề tài " A C2-smooth counterexample to the Hamiltonian Seifert conjecture in R4 "

We construct a proper C 2 -smooth function on R4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C 2 -smooth counterexample to the Hamiltonian Seifert conjecture in dimension four. 1. Introduction The “Hamiltonian Seifert conjecture” is the question whether or not there exists a proper function on R2n whose Hamiltonian flow has no periodic orbits on at least one regular level set. | Annals of Mathematics A C2-smooth counterexample to the Hamiltonian Seifert conjecture in R4 By Viktor L. Ginzburg and Basnak Z. G urel Annals of Mathematics 158 2003 953 976 A C2-smooth counterexample to the Hamiltonian Seifert conjecture in R4 By Viktor L. Ginzburg and Basak Z. Gurel Abstract We construct a proper C2-smooth function on R4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four. 1. Introduction The Hamiltonian Seifert conjecture is the question whether or not there exists a proper function on R2ra whose Hamiltonian flow has no periodic orbits on at least one regular level set. We construct a C2-smooth function on R4 with such a level set. Following the tradition of Gi4 He1 He2 Ke KuG KuGK KuK1 KuK2 Sc we can call this result a C2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four. We emphasize that in this example the Hamiltonian vector field is C 1-smooth while the function is C2 . In dimensions greater than six C -smooth counterexamples to the Hamiltonian Seifert conjecture were constructed by one of the authors Gi1 and simultaneously by M. Herman He1 He2 . In dimension six a C21 -smooth counterexample was found by M. Herman He1 He2 . This smoothness constraint was later relaxed to C x in Gi2 . A very simple and elegant construction of a new C x-smooth counterexample in dimensions greater than four was recently discovered by E. Kerman Ke . The flow in Kerman s example has dynamics different from the ones in Gi1 Gi2 He1 He2 . We refer the reader to Gi3 Gi4 for a detailed discussion of the Hamiltonian Seifert conjecture. The reader interested in the results concerning the original Seifert conjecture settled by K. Kuperberg KuGK KuK1 should consult KuK2 KuK3 . Here we only mention that a C 1-smooth counterexample to the Seifert conjecture on S3 was constructed by P. Schweitzer Sc

• Thạc sĩ - Tiến sĩ - Cao học
• counterexample
• subjects of mathematics
• Annals of Mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• A counterexample to the strong version of Freedmans conjecture
• tài liệu báo cáo nghiên cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• công trình toán học
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center