相关论文: Local perturbations of conservative $C^1$-diffeomo…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
We show how the local approximation of astrophysical discs, which is the basis for the well known model of the shearing box, can be used to study many aspects of the dynamics of warped discs. In the local model, inclination of the orbit of…
We investigate perturbations in the Kepler problem. We offer an overview of the dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics to build a foundation for analyzing perturbations. We consider the effects of a…
Asaoka & Irie recently proved a $C^{\infty}$ closing lemma of Hamiltonian diffeomorphisms of closed surfaces. We reformulated their techniques into a more general perturbation lemma for area-preserving diffeomorphism and proved a…
In this work, we investigate diffeomorphisms whose positiveness of topological entropy is destroyed by singular suspensions. We show that this phenomenon is rare in the set of $C^1$-diffeomorphisms. Precisely, we prove that for an open and…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
The main result of this work is the following: for volume preserving flows on compact manifolds with the $C^r$ topology, $1 \leqq r \leqq \infty$ , the closure of every invariant manifold of periodic orbits and singularities is a chain…
The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is…
To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or…
Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The…
We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…
In this work, we investigate the dynamics of homeomorphisms through the lens of the local shadowing theory. We study the influence of positively shadowable points and positively shadowable measures into the local entropy theory of…
We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
A diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a $C^1$-neighbourhood $\cU$ of $f$ such that every diffeomorphism in $g\in \cU$ has a hyperbolic set $\La_g$, depending continuously on $g$, such that the stable and…
For partially hyperbolic diffeomorphisms with mostly expanding and mostly contracting centers, we establish a topological structure, called skeleton{a set consisting of finitely many hyperbolic periodic points with maximal cardinality for…
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…
This paper gives a survey of recent results on the maximal transitive sets of $C^1$-generic diffeomorphisms.
We discuss the use of differential sampling method to image local perturbations in anisotropic periodic layers, extending earlier works on the isotropic case. We study in particular the new interior transmission problem that is associated…