PPT-Order and Chaos in 2-Dimensional Area-Preserving Maps

Zhumagali Shomanov Evangelos Mitsokapas Shirali Kadyrov Anastasios Bountis Overview An introduction to the Standard Map The transition from regular to chaotic motion Box counting dimensions and qGaussian distributions. Perturbation theory. Quasi integrable Hamiltonians . Small divisor problem. KAM theorem, . Melnikov’s. integral. Numerical measurements of . Lyapunov. exponents. Nekhoroshev. . Theorm. Chirikov. Jirkovsky. 1. and Luis Maria Bo-oT. 2,*. 1. Department of Informatics and Geo-informatics, . Fakulta. . Zivotnivo. . Prostedi. , . Univ. of J.E. . Purkyne. , . Kralova. . Vysina. 7, . Usti n. L., 40096 Czech Republic. Historical Maps. The oldest map?. Konya . town map, Turkey, c. 6200 BC. Milestones Project. http://www.math.yorku.ca/SCS/Gallery/milestone/. The First World Map. Anaximander of Miletus, Turkey, c. 550 BC. spline. Methods for the Incompressible . Navier. -Stokes Equations. John Andrew Evans. Institute for Computational Engineering and Sciences, UT Austin. Stabilized and . Multiscale. . Methods in CFD. Module 14 Lesson 2. Review of Two-Dimensional and Three-Dimensional Figures. A Two-Dimensional (2D) shape is a . shape that only has two . dimensions: . width and . height.. Examples: Squares. , Circles, Triangles, etc are two dimensional objects. How to Combine Counties, . Split . Counties, . &. use . Zip Code Boundaries . Rick Andrews. Office of the Actuary. Centers for Medicare and Medicaid Services. Robert Allison. Research and Development. Introduction to . Maps. What . is. a map?. A generalized view of an area, usually some portion of Earth’s surface, as seen from above at a greatly reduced size. Any geographical image of the environment. pz.tt/CSUN16-map. Dyslexia. Moderate vision impairment. Severe vision impairment. Epilepsy. Migraines. Physical impairment. Fibromyalgia. Multiple Sclerosis. Crohns. Disease. PTSD. Aspergers. It’s not just . How to Combine Counties, . Split . Counties, . &. use . Zip Code Boundaries . Rick Andrews. Office of the Actuary. Centers for Medicare and Medicaid Services. Robert Allison. Research and Development. Temple . and . Calendar. Intellectual Adjustment. Mythic. Thinking . Does not mean biblical stories are “fairy tales”. Refers to symbolic metaphors used to make concepts comprehensible. Bible has many of them – visual metaphors that . & Types of maps. Map projections. Map projections. Cartographers have to deal with the problem of making maps of a spherical earth onto a flat surface .  this leads to . distortions. Shape can be distorted. We will pose and answer geographic questions about our planet, the distribution and patterns for various world regions and countries, economic activities, and society’s ability to control territory using many different graphic tools.. TOPIC-MAPS. GEOGRAPHY. CLASS-VI. WHAT ARE MAPS?. A map can be defined as a two dimensional representation of the whole or part of the earth drawn to scale on a flat surface.. A collection of maps is called an atlas. The oldest map?. Konya . town map, Turkey, c. 6200 BC. Milestones Project. http://www.math.yorku.ca/SCS/Gallery/milestone/. The First World Map. Anaximander of Miletus, Turkey, c. 550 BC. Milestones Project.