Nongeneric Bifurcations Near a Nontransversal Heterodimensional Cycle

In this paper bifurcations of heterodimensional cycles with highly degenerate conditions are studied in three dimensional vector fields,where a nontransversal intersection between the two-dimensional manifolds of the saddle equilibria occurs.By setting up local moving frame systems in some tubular neighborhood of unperturbed heterodimensional cycles,the authors construct a Poincar′e return map under the nongeneric conditions and further obtain the bifurcation equations.By means of the bifurcation equations,the authors show that different bifurcation surfaces exhibit variety and complexity of the bifurcation of degenerate heterodimensional cycles.Moreover,an example is given to show the existence of a nontransversal heterodimensional cycle with one orbit flip in three dimensional system.     

人造卫星运行轨道的实时仿真技术

人造卫星在星空背景下运行的实时仿真技术中,建模和实时性是仿真的基础,试验表明,利用Creator 2.6建立二体轨道下的卫星运行模型,计算出卫星运行时的空间位置和运动姿态,结合Vega Prime来实现人造卫星运动轨道的空间动态三维场景实时仿真,可以有效的实现卫星在星空背景运动中的实时性,并为其他技术领域中的实物或半实物实时仿真技术提供了可行性的参考方法.     

Explicit Classifications of Orbits in Jordan Algebra and Freudenthal Vector Space Over the Exceptional Lie Groups

ABSTRACT

We give the explicit classifications of orbits in the Jordan algebra 𝔍 over the group E _6(?26) and the Freudenthal, R -vector space 𝔓 over the group E _7(?25).

Communicated by E. Zelmanov     

On Rings with Few Orbits

In this article we investigate the structure of rings with some strong symmetry condition.     

Expanding Periodic Orbits with Small Exponents

It is shown that the growth rate of the number of expanding periodic orbits with small Lyapunov exponents is strictly smaller than the topological entropy for any C 1 map in dimension one.     

Additive Decomposition of Real Matrices

The orthogonal orbit ${\cal O}(A)$ of an n × n real matrix A is the set of real matrices of the form $P^t \ AP$ where $P^t P = I_n$ . We show that $A/ \| A\|$ is an affine sum of four orthogonal matrices, and note that $A^t$ can always be written as an affine combination of no more than 2 n m 1 matrices in ${\cal O}(A)$ . This improves some recent results of Zhan, and answers some of his questions. Other related results are also discussed.     

Conformal mechanics

The SL(2,R)$SL(2,\mathbb{R})$ invariant Hamiltonian systems are discussed within the framework of the orbit method. It is shown that both the dynamics and the symmetry transformations are globally well-defined on phase space. The flexibility in the choice of the time variable and the Hamiltonian function described in the paper by de Alfaro et al. [Nuovo Cimento 34A (1976) 569] is related to the nontrivial global structure of 1+0$1+0$-dimensional space–time. The operational definition of time is discussed.