Zobrazeno 1 - 10
of 161
pro vyhledávání: '"Knauf, Andreas"'
Autor:
Knauf, Andreas
We consider the Kepler potential and its relatives $q\mapsto -\|q\|^{-2(1-1/n)}$, $n\in\mathbb{N}$ in arbitrary dimension $d$. We derive a unique real-analytic symplectic extension of phase space on which the Hamiltonian flow is complete and still re
Externí odkaz:
http://arxiv.org/abs/2408.00877
Autor:
Knauf, Andreas, Montgomery, Richard
For n bodies moving in Euclidean d-space under the influence of a homogeneous pair interaction we compactify every center-of-mass energy surface, obtaining a 2d(n -1)-1 - dimensional manifold with corners in the sense of Melrose. After a time change,
Externí odkaz:
http://arxiv.org/abs/2307.03837
We consider the scattering of $n$ classical particles interacting via pair potentials, under the assumption that each pair potential is "long-range", i.e. being of order ${\cal O}(r^{-\alpha})$ for some $\alpha >0$. We define and focus on the "free r
Externí odkaz:
http://arxiv.org/abs/2103.13717
Autor:
Knauf, Andreas, Martynchuk, Nikolay
Classical Morse theory proceeds by considering sublevel sets $f^{-1}(-\infty, a]$ of a Morse function $f: M \to R$, where $M$ is a smooth finite-dimensional manifold. In this paper, we study the topology of the level sets $f^{-1}(a)$ and give conditi
Externí odkaz:
http://arxiv.org/abs/1910.05294
Autor:
Knauf, Andreas
Asymptotic velocity is defined as the Ces\`aro limit of velocity. As such, its existence has been proven for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here we show for a class of pair p
Externí odkaz:
http://arxiv.org/abs/1811.08266
Autor:
Fleischer, Stefan, Knauf, Andreas
Given a volume preserving dynamical system with non-compact phase space, one is sometimes interested in special subsets of its wandering set. One example from celestial mechanics is the set of initial values leading to collision. Another one is the s
Externí odkaz:
http://arxiv.org/abs/1802.08566
Autor:
Fleischer, Stefan, Knauf, Andreas
For a wide class of two-body interactions, including standard examples like gravitational or Coulomb fields, we show that collision orbits in $n$-body systems are of Liouville measure zero for all energies. We use techniques from symplectic geometry
Externí odkaz:
http://arxiv.org/abs/1802.08564
Autor:
Knauf, Andreas, Seri, Marcello
Publikováno v:
Regular and Chaotic Dynamics, Issue 4, Vol. 22 (2017)
For n convex magnetic bumps in the plane, whose boundary has a curvature somewhat smaller than the absolute value of the constant magnetic field inside the bump, we construct a complete symbolic dynamics of a classical particle moving with speed one.
Externí odkaz:
http://arxiv.org/abs/1612.03670
Motivated by the high-energy limit of the $N$-body problem we construct non-deterministic billiard process. The billiard table is the complement of a finite collection of linear subspaces within a Euclidean vector space. A trajectory is a constant sp
Externí odkaz:
http://arxiv.org/abs/1606.01420
Autor:
Knauf, Andreas
We introduce and consider the notion of stable degeneracies of translation invariant energy functions for finite Ising models. By this term we mean the lack of injectivity that cannot be lifted by changing the interaction. We show that besides the sy
Externí odkaz:
http://arxiv.org/abs/1508.04293