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Singularities and nonhyperbolic manifolds do not coincide
Semi-dispersing billiards hyperbolicity ergodicity local ergodicity invariant manifolds Chernov–Sinai Ansatz
2012/5/9
We consider the billiard flow of elastically colliding hard disks on the flat 2-torus and prove that no singularity manifold can locally coincide with a manifold describing future non-hyperbolicity of...
司建国，1958年12月生；教授、博士生导师。研究兴趣：常微分方程定性理论、哈密顿动力系统、KAM理论、迭代泛函微分方程的解析理论。
Asymptotic expansion of smooth interval maps
Asymptotic expansion smooth interval maps Dynamical Systems
2012/4/16
We show that several different ways to quantify the asymptotic expansion of a non-degenerate smooth interval map coincide. A consequence is an extension to multimodal maps of the remarkable result of ...
On superintegrable Stackel systems: elliptic and parabolic coordinates
superintegrable Stackel systems elliptic and parabolic coordinates Dynamical Systems
2012/4/26
Recently we proposed a generic construction of the additional integrals of motion for the Stackel systems applying addition theorems to the angle variables. In this note we show some trivial examples ...
Liouville-Arnold integrability for scattering under cone potentials
Liouville-Arnold integrability scattering cone potentials Dynamical Systems
2012/4/26
The problem of scattering of particles on the line with repulsive interactions, gives rise to some well-known integrable Hamiltonian systems, for example, the nonperiodic Toda lattice or Calogero's sy...
A class of integrable Hamiltonian systems including scattering of particles on the line with repulsive interactions
class of integrable Hamiltonian systems scattering of particles line repulsive interactions
2012/4/26
The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the as...
Etude d'un modele de dynamique des populations
Etude d'un modele dynamique des populations Dynamical Systems
2012/4/23
We study an infinite dimensional dynamical system that was proposed by J.C. Yoccoz and N.G. Yoccoz for modeling the population dynamics of some small rodents. We show an attractor exist in a large dom...
Symmetries of Julia sets of polynomial skew products on C^2
Complex dynamics skew product Green function
2012/4/18
We consider the symmetries of Julia sets of polynomial skew products on C^2, which are birationally conjugate to rotational products. Our main results give the classification of the polynomial skew pr...
Integrability of higher pentagram maps
Integrability of higher pentagram maps Dynamical Systems
2012/4/23
We define higher pentagram maps on polygons in $P^d$ for any dimension $d$, which extend R.Schwartz's definition of the 2D pentagram map. We prove their integrability for both closed and twisted polyg...
Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
partial hyperbolicity singular-hyperbolicity recurrence decay of correlations local dimension hitting times
2012/4/23
We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue...
Special representations of nilpotent Lie groups and the associated Poisson representations of current groups
Current group canonical representation special representation
2012/4/18
In this paper we describe the new model of the representations of the current groups with a semisimple Lie group of the rank one. In the earlier papers of 70-80-th (Araki, Gelfand-Graev-Vershik) had p...
Banach representations and affine compactifications of dynamical systems
affine compactification affine flow Asplund space enveloping semigroup non-sensitivity right topological semigroup
2012/4/18
To every Banach space V we associate a compact right topological affine semigroup E(V). We show that a separable Banach space V is Asplund if and only if E(V) is metrizable, and it is Rosenthal (i.e. ...
Fundamental domain of invariant sets and applications
Fundamental domain partial hyperbolicity cocycle transitivity accessibility essential saturation
2012/4/18
Let $X$ be a compact metric space and $f:X\to X$ a homeomorphism on $X$. We construct a fundamental domain for the set with finite peaks for each cocycle induced by $\phi\in C(X,R)$. In particular we ...
Contracting Quadratic Operators of Bisexual Population
Quadratic stochastic operator fixed point trajectory contracting operators
2012/4/18
In this paper we find a sufficient condition under which the operator of bisexual population is contraction and show that this condition is not necessary.
Entropy, Lyapunov exponents and the volume growth of boundary distortion under the action of dynamical systems
Lyapunov exponents the volume growth of boundary distortion the action of dynamical systems
2012/4/17
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.