Related papers: Dynamics of multicritical circle maps

We revisit the well-established regularity estimates on harmonic maps on surfaces to question their independence with respect to the dimension of the target manifold. We are mainly interested in harmonic maps into target ellipsoids, that we…

Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found…

The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of…

In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed number of iterations and symbolic…

We show a flexibility result in the context of generalized entropy. The space of dynamical systems we work with is, homeomorphisms on the sphere whose non-wandering set consist in only one fixed point.

Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…

For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit…

The monograph is concerned with some key problems of the theory of nonlinear economic dynamics. The authors' concept consists in analyzing the problem of structural instability of economic systems within the framework of the synergetic…

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…

We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the…

We use simple models (the Ising model in one and two dimensions, and the spherical model in arbitrary dimension) to put to the test some recent ideas on the slow dynamics of nonequilibrium systems. In this review the focus is on the…

An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over an arbitrary finite field. For systems that can be…

In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…

In the 1960s and 1970s a large part of the theory of dynamical systems concerned the case of uniformly hyperbolic or Axiom A dynamical system and abstract ergodic theory of smooth dynamical systems. However since around 1980 an emphasize…

The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental…

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…

We expand the dictionary between the action of a torus homeomorphism on the fine curve graph and its rotation set. More precisely, we show that the fixed points at infinity of a loxodromic element determine the rotation set up to scale. A…

Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…

In this paper, we investigate some dynamical properties near a nonhyperbolic fixed point. Under some conditions on the higher nonlinear terms, we establish a stable manifold theorem and a degenerate Hartman theorem. Furthermore, the finite…

We study discrete fixed point sets of holomorphic self-maps of complex manifolds. The main attention is focused on the cardinality of this set and its configuration. As a consequence of one of our observations, a bounded domain in ${\Bbb…