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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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Density of orbits and arithmetic degrees of automorphisms of projective threefolds
射影三重 轨道密度 自同构 算术度
2023/4/18
The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Linked periodic orbits of disc homeomorphisms
圆盘同胚 连锁 周期轨道
2023/5/8
In 1990, Gambaudo introduced the notion of linking of two invariant sets of a surface self-map. Most of the known results of linked periodic orbits are about an orbit linked with a fixed point. In thi...
In this paper we develop a symbolic dynamics approach to a problem
of studing of dimensional characteristics of the set of bounded geodesics on
manifolds of negative curvature.
An outer billard map F is defined outside a closed convex curve Γ in the
following way. Let z be a point on the plane. Consider the supporting
line L(z) from z to Γ such that Γ lies on the rig...
This paper is the sequel to The radiance obstruction and par-
allel forms on a;ffne manifolds (lYans. Amer. Math. Soc. 286 (1984),
629 649) which introduced a new family of secondary characteristi...
Orbits of nearly integrable systems accumulating to KAM tori
nearly integrable systems KAM tori
2015/9/25
Orbits of nearly integrable systems accumulating to KAM tori.
Periodic Orbits of Hybrid Systems and Parameter Estimation via AD
Hybrid Systems Parameter Estimation via AD
2015/8/25
Rhythmic, periodic processes are ubiquitous in biological systems; for example,
the heart beat, walking, circadian rhythms and the menstrual cycle. Modeling
these processes with high delity as peri...
HOMOCLINIC ORBITS OF THE FITZHUGH-NAGUMO EQUATION: THE SINGULAR-LIMIT
FITZHUGH-NAGUMO EQUATION SINGULAR-LIMIT
2015/8/25
The FitzHugh-Nagumo equation has been investigated with a wide
array of different methods in the last three decades. Recently a version of
the equations with an applied current was analyzed by Champ...
Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System
homoclinic bifurcation singular perturbation
2015/8/25
This paper investigates travelling wave solutions of the FitzHugh–Nagumo equation from the viewpoint
of fast-slow dynamical systems. These solutions are homoclinic orbits of a three dimensional
vect...
Computing Periodic Orbits and their Bifurcations with Automatic Differentiation
Automatic Differentiation Computing Periodic Orbits
2015/8/25
This paper examines algorithms for computing periodic orbits of dynamical systems. Our
goal is to explore the limits of accuracy that are attainable for these calculations within
the pragmatic conte...
Periodic Orbits of Vector Fields: Computational Challenges
Computational Challenges Vector Fields
2015/8/25
Simulation of vector elds is ubiquitous: examples occur in every discipline of
science and engineering. Periodic orbits are frequently encountered as trajectories.
We use solutions of initial value...
The dynamics of
uids are often studied through the reduction of partial di erential
equations to systems with only a few degrees of freedom. Analysis of these low dimensional
vector elds remains ...
Iteration theory of Maslov-type index associated with a Lagrangian subspace for symplectic paths and Multiplicity of brake orbits in bounded convex symmetric domains
Iteration theory Maslov-type index Lagrangian subspace symplectic paths and Multiplicity brake orbits in bounded convex symmetric domains
2015/4/3
Iteration theory of Maslov-type index associated with a Lagrangian subspace for symplectic paths and Multiplicity of brake orbits in bounded convex symmetric domains.
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit
Index and Stability of Symmetric Periodic Orbits Hamiltonian Systems Application to Figure-Eight Orbit
2015/4/3
Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit.