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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Proofs of two or infinity conjectures for Reeb orbits and closed geodesics
Reeb轨道 闭测地线 两个 无穷大猜想
2023/11/29
In this talk, we give a proof of the conjecture of Hofer-Wysocki-Zehnder published in 2003 asserting that a smooth and autonomous Hamiltonian flow on R4 has either two or infinitely many simple period...
Lagrange Stabilization of Pendulum-like Systems: A Pseudo H-infinity Control Approach
Pseudo Strict Bounded Real Lemma Pendulum-like systems Lagrange stability
2011/10/10
Abstract: This paper studies the Lagrange stabilization of a class of nonlinear systems whose linear part has a singular system matrix and which have multiple periodic (in state) nonlinearities. Both ...
The M/M/Infinity Service System with Ranked Servers in Heavy Traffic
Queueing theory asymptotic expansions Probability
2011/8/30
Abstract: We consider an M/M/Infinity service system in which an arriving customer is served by the first idle server in an infinite sequence S_1, S_2, ... of servers. We determine the first two terms...
Spectral and stochastic properties of the $f$-Laplacian, solutions of PDE's at infinity, and geometric applications
Weighted Laplacians Feller property stochastic completeness essential spectrum gradient Ricci solitons
2011/8/26
Abstract: The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come from spec...
The classification of polynomial basins of infinity
polynomial basins of infinity Dynamical Systems Complex Variables
2011/8/26
Abstract: We consider the problem of classifying the dynamics of complex polynomials $f: \mathbb{C} \to \mathbb{C}$ restricted to their basins of infinity. We synthesize existing combinatorial tools -...
Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces
Moebius structures Ptolemy spaces boundary at infinity of complex hyperbolic spaces
2011/1/19
The paper initiates a systematic study of M¨obius structures and Ptolemy spaces. We conjecture that every compact Ptolemy space with circles and many space inversions is M¨obius equivalent to the boun...
Cech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction
Cech cocycles differential characteristic classes
2010/11/24
We define for every L-infinity algebra a smooth infinity-group integrating it, and define smooth principal infinity-bundles with connection. For every L-infinity-algebra cocycle of suitable degree, we...
On the injectivity radius and tangent cones at infinity of gradient Ricci solitons
injectivity radius tangent cones infinity of gradient Ricci solitons
2011/1/18
A lower-bound estimate of injectivity radius for complete Riemannian manifolds is discussed in a pure geometric viewpoint and is applied to study tangent cones at in nity of certain gradient Ricci sol...
We adapt the classical framework of algebraic theories to work in the setting of (infinity,1)-categories developed by Joyal and Lurie. This gives a suitable approach for describing highly structured o...
Non-Local Tug-of-War and the Infinity Fractional Laplacian
Non-Local Tug-of-War the Infinity Fractional Laplacian
2010/11/15
Motivated by the "tug-of-war" game studied in [12], we consider a "non-local" version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of f...
Concentration on circles for nonlinear Schrödinger-Poisson systems with unbounded potentials vanishing at infinity
Stationary nonlinear Schrö dinger-Poisson system weighted Sobolev spaces
2010/12/6
The present paper is devoted to weighted Nonlinear Schrödinger- Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the exi...
Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity
Kleinian groups Poincar´ e exponent fractal geometry dissipative dy-namics
2010/11/29
The main result of this paper is to show that if N is a normal subgroup of a Kleinian group G such that G/N contains a coset which is represented by some loxodromic element, then the Hausdorff dimensi...
Curved infinity-algebras and their characteristic classes
Curved infinity-algebras characteristic classes
2010/12/15
In this paper we study a natural extension of Kontsevich’s characteristic class
construction for A∞- and L∞-algebras to the case of curved algebras. These define homology
classes on a variant of his...
Degenerate homogeneous parabolic equations associated with the infinity-Laplacian
Degenerate homogeneous parabolic equations infinity-Laplacian
2010/12/8
We prove existence and uniqueness of viscosity solutions to the degenerate parabolic problem ut = h 1u where h 1 is the h-homogeneous operator associated with the infinity-Laplacian, h 1u = |Du|h&#...
The Infinity of Complete Riemannian Manifolds under Yamabe Flow
Yamabe flow locally conformally flat asymptotic volume ratio
2018/4/19
We study complete locally conformally flat Riemannian manifolds Mn.We prove that the flatness of the infinity geometry can be preserved under the Yamabe flow. As an immediate application, the asymptot...