Listing 1 - 5 of 5 |
Sort by
|
Choose an application
Combinatorial dynamics. --- Differential equations. --- Dynamics --- Mathematics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- 517.91 Differential equations --- Differential equations --- Dynamics, Combinatorial --- Periodic orbits, Types of (Mathematics) --- Types of periodic orbits (Mathematics) --- Differentiable dynamical systems --- Dinàmica combinatòria --- Sistemes dinàmics diferenciables
Choose an application
This book provides a comprehensive survey of the Sharkovsky ordering, its different aspects and its role in dynamical systems theory and applications. It addresses the coexistence of cycles for continuous interval maps and one-dimensional spaces, combinatorial dynamics on the interval and multidimensional dynamical systems. Also featured is a short chapter of personal remarks by O.M. Sharkovsky on the history of the Sharkovsky ordering, the discovery of which almost 60 years ago led to the inception of combinatorial dynamics. Now one of cornerstones of dynamics, bifurcation theory and chaos theory, the Sharkovsky ordering is an important tool for the investigation of dynamical processes in nature. Assuming only a basic mathematical background, the book will appeal to students, researchers and anyone who is interested in the subject.
Topology --- Functional analysis --- Differential equations --- Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- differentiaalvergelijkingen --- mathematische modellen --- wiskunde --- fysica --- topologie --- dynamica
Choose an application
"The so-called "pinched disk" model of the Mandelbrot set is due to A. Douady, J. H. Hubbard and W. P. Thurston. It can be described in the language of geodesic laminations. The combinatorial model is the quotient space of the unit disk under an equivalence relation that, loosely speaking, "pinches" the disk in the plane (whence the name of the model). The significance of the model lies in particular in the fact that this quotient is planar and therefore can be easily visualized. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated MLC conjecture stating that the Mandelbrot set is locally connected. For parameter spaces of higher degree polynomials no combinatorial model is known. One possible reason may be that the higher degree analog of the MLC conjecture is known to be false. We investigate to which extent a geodesic lamination is determined by the location of its critical sets and when different choices of critical sets lead to essentially the same lamination. This yields models of various parameter spaces of laminations similar to the "pinched disk" model of the Mandelbrot set"--
Geodesics (Mathematics) --- Polynomials. --- Invariant manifolds. --- Combinatorial analysis. --- Dynamics. --- Géodésiques (mathématiques) --- Polynômes. --- Variétés invariantes. --- Analyse combinatoire. --- Dynamique.
Choose an application
Dinàmica combinatòria --- Sistemes dinàmics diferenciables --- Combinatorial dynamics. --- Differential equations. --- Dynamics --- Mathematics.
Choose an application
Topology --- Fixed point theory. --- Théorème du point fixe --- 51 <082.1> --- Mathematics--Series --- Théorème du point fixe --- Fixed point theory --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics)
Listing 1 - 5 of 5 |
Sort by
|