Hamiltonian Chaos

2019 ◽  
pp. 154-176
Author(s):  
David D. Nolte
Keyword(s):  
Quantum Chaos ◽  
Kam Theory ◽  
Rigid Rotator ◽  
Standard Map ◽  
Web Map ◽  
Classical Chaos ◽  
Hamiltonian Chaos ◽  
Area Preserving Maps ◽  
Area Preserving ◽  
The Web

Nondissipative or Hamiltonian systems are also capable of chaos as phase space volume is twisted and folded in area-preserving maps like the Standard Map. When nonintegrable terms are added to a potential function, Hamiltonian chaos emerges. The Standard Map (also known as the Chirikov map) for a periodically kicked rigid rotator provides a simple model with which to explore the emergence of Hamiltonian chaos as well as the KAM theory of islands of stability. A periodically kicked harmonic oscillator displays extended chaos in the web map. Hamiltonian classical chaos makes a direct connection to quantum chaos, which is illustrated using the chaotic stadium, for which quantum scars are associated with periodic classical orbits in the stadium.

Homoclinic Orbits in the Complex Domain

1997 ◽  
Vol 07 (02) ◽  
pp. 253-274 ◽  
Author(s):  
V. F. Lazutkin ◽  
C. Simó
Keyword(s):  
Homoclinic Orbits ◽  
Homoclinic Tangency ◽  
Complex Domain ◽  
Standard Map ◽  
Homoclinic Points ◽  
Promising Tool ◽  
Theoretical Support ◽  
Area Preserving Maps ◽  
Area Preserving

We consider the standard map, as a paradigm of area preserving map, when the variables are taken as complex. We study how to detect the complex homoclinic points, which cannot dissappear under a homoclinic tangency. This seems a promising tool to understand the stochastic zones of area preserving maps. The paper is mainly phenomenological and includes theoretical support to the observed phenomena. Several conjectures are stated.

scholarly journals Hamiltonian Maps for Heliac Magnetic Islands

1995 ◽  
Vol 48 (5) ◽  
pp. 871 ◽  
Author(s):  
MG Davidson ◽  
RL Dewar ◽  
HJ Gardner ◽  
J Howard
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Chaos Theory ◽  
Magnetic Islands ◽  
Twist Map ◽  
Hamiltonian Chaos ◽  
Area Preserving Maps ◽  
Vacuum Fields ◽  
Rotational Transform ◽  
Area Preserving

Magnetic islands in toroidal heliac stellarator vacuum fields are explored with Hamiltonian chaos theory and the associated area-preserving maps. Magnetic field line island chains are examined first analytically, with perturbation theory, and then numerically to produce Poincaré sections, which are compared with H−1 Heliac stellarator puncture plot diagrams. Rotational transform profiles are chosen to permit the comparison of twist map and nontwist map predictions with field line behaviour computed by a field line tracing computer program and observed experimentally.

scholarly journals Extensive Numerical Results for Integrable Case of Standard Map

2020 ◽  
Vol 23 (2) ◽  
pp. 149-152
Author(s):  
Ugur Tirnakli ◽  
Constantino Tsallis
Keyword(s):  
Mechanical Characterization ◽  
Initial Conditions ◽  
Random Variable ◽  
Integrable Case ◽  
Standard Map ◽  
Region Of Stability ◽  
Area Preserving Maps ◽  
Statistical Mechanical ◽  
Area Preserving ◽  
Special Case

In recent years, conservative dynamical systems have become a vivid area of research from the statistical mechanical characterization viewpoint. With this respect, several areapreserving maps have been studied. It has been numerically shown that the probability distribution of the sum of the suitable random variable of these systems can be well approximated by a Gaussian (q-Gaussian) when the initial conditions are randomly selected from the chaotic sea (region of stability islands) in the available phase space. In this study, we will summarize these results and discuss a special case for the standard map, a paradigmatic example of area-preserving maps, for which the map is totally integrable.

scholarly journals CREATION OF THE WEB-MAP OF THE BOGUSLAVSKY DISTRICT

2019 ◽  
pp. 129-139
Author(s):  
Tamara Mykolayivna Kurach ◽  
Iryna Aleksandrovna Pidlisetskaya
Keyword(s):  
Cultural Heritage ◽  
Theoretical Basis ◽  
Large Scale ◽  
Web Mapping ◽  
Heritage Sites ◽  
Web Map ◽  
Thematic Mapping ◽  
Interactive Map ◽  
The Web

The goal is to develop a tourist interactive map "Landmarks of Bohuslav". The methodology. The methodological and theoretical basis of the study is modern geographical and cartographic science in the field of thematic mapping with the involvement of web-mapping technologies. Results. A large-scale tourist web map of the cultural heritage of the Boguslavsky region - “Sights of Boguslavshchina” was created. Scientific novelty. Approbation of the methodology and technology for the development of interactive large-scale web maps of tourism topics involving the Leaflet JavaScript library. Practical value. An interactive tourist web map of the historical and cultural heritage sites “Sights of Bohuslavshchina” will be published on the website of the health-improving institution of sanatorium-type “Chaika”. Convenient using, visualization, prompt receipt of information will help to increase the attractiveness of tourist Boguslavschina routes.

scholarly journals Performance Testing of Web Map Services tn three Dimensions – X, Y, Scale

2013 ◽  
Vol 21 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Dušan Cibulka
Keyword(s):  
Performance Testing ◽  
Service Performance ◽  
Performance Characteristics ◽  
Three Dimensions ◽  
Web Mapping ◽  
Practical Experiment ◽  
Web Map ◽  
Open Geospatial Consortium ◽  
Map Service ◽  
The Web

Abstract The paper deals with the performance testing of web mapping services. The paper describes map service tests in which it is possible to determine the performance characteristics of a map service, depending on the location and scale of the map. The implementation of the test is tailored to the Web Map Service specifications provided by the Open Geospatial Consortium. The practical experiment consists of testing the map composition acquired from OpenStreetMap data for the area of southwestern Slovakia. These tests permit checking the performance of services in different positions, verifying the configuration of services, the composition of a map, and the visualization of geodata. The task of this paper is to also highlight the fact that it is not sufficient to only interpret a map service performance with conventional indicators. A map service’s performance should be linked to information about the map’s scale and location.

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