相关论文: Statistical properties of unimodal maps: physical …
We study the arc complex of a surface with marked points in the interior and on the boundary. We prove that the isomorphism type of the arc complex determines the topology of the underlying surface, and that in all but a few cases every…
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic dissipative systems; analogous to sums over periodic orbits…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we…
We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. But a…
We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional…
When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: parity, global…
We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in…
Brake orbits and homoclinics of autonomous dynamical systems correspond, via Maupertuis principle, to geodesics in Riemannian manifolds endowed with a metric which is singular on the boundary (Jacobi metric). Motivated by the classical, yet…
The aim of the paper is to clarify the nature of combinatorial structures associated with maps on closed compact surfaces. We prove that maps give rise to Lagrangian matroids representable in a setting provided by cohomology of the surface…
An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…
This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\in\Diff(M)$. We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages…
Conformally symplectic diffeomorphisms $f:M \rightarrow M$ transform a symplectic form $\omega$ on a manifold M into a multiple of itself, $f^* \omega = \eta \omega$. We assume $\omega$ is bounded, as some of the results may fail otherwise.…
This survey reviews results on harmonic maps into spaces of non-positive curvature, with a focus on targets that lack smooth structure. More precisely, we consider targets that are complete metric spaces with non-positive curvature in the…
A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on…
The Milnor problem on one-dimensional attractors is solved for S-unimodal maps with a non-degenerate critical point c. It provides us with a complete understanding of the possible limit behavior for Lebesgue almost every point. This theorem…
In this paper we prove that the monotonicity of kneading sequences and topological entropy, a fundamental structural property of the quadratic family, extends to the class of power-law unimodal maps $f_a(x)=a-|x|^r$ for arbitrary critical…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…