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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
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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
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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
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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...
Basic results in the rigorous theory of weighted dynamical zeta functions
or dynamically defined generalized Fredholm determinants are presented. Analytic
properties of the zeta functions or d...
BOUNDED ORBITS OF ANOSOV FLOWS
ANOSOV FLOWS BOUNDED ORBITS
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2015/9/29
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
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2015/9/25
Orbits of nearly integrable systems accumulating to KAM tori.
Are artificial satellites orbits influenced by an expanding Earth?
orbit perturbations expanding Earth
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2015/9/7
Albeit in the past great theoretical and experimental efforts were made in proposing and searching for G time-decreasing, a major role could be played by an increase of M. A recent analysis (Scalera, ...
Periodic Orbits of Hybrid Systems and Parameter Estimation via AD
Hybrid Systems Parameter Estimation via AD
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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
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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
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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
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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
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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 ...