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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Objectives of the Study
1.3 Limitations of the Study
1.4 Scope of the Study

Chapter 2: Literature Review
2.1 Theoretical Foundations of Invariant Manifolds
2.2 Previous Studies on Approximating Invariant Manifolds
2.3 Applications of Invariant Manifolds in Hamiltonian Systems

Chapter 3: Research Methodology
3.1 Data Collection Methods
3.2 Data Analysis Techniques
3.3 Computational Tools Used for Approximating Invariant Manifolds

Chapter 4: Discussion of Findings
4.1 Analysis of Approximated Invariant Manifolds
4.2 Comparison of Different Methods for Approximating Invariant Manifolds
4.3 Interpretation of Results in the Context of Hamiltonian Systems

Chapter 5: Conclusion and Summary
5.1 Summary of Key Findings
5.2 Contributions to the Field
5.3 Recommendations for Future Research

Brief Overview:

The thesis titled “Approximating Invariant Manifolds of Hamiltonian Systems” explores the concept of invariant manifolds and their approximation in the context of Hamiltonian systems. In Chapter 1, the introduction provides a background of the study, outlines the objectives, limitations, and scope of the research.

Chapter 2 delves into the theoretical foundations of invariant manifolds, reviews previous studies on approximating invariant manifolds, and discusses the applications of invariant manifolds in Hamiltonian systems.

The research methodology in Chapter 3 details the data collection methods, data analysis techniques, and computational tools used for approximating invariant manifolds. Chapter 4 presents the discussion of findings, including the analysis of approximated invariant manifolds, comparison of different approximation methods, and interpretation of results in the context of Hamiltonian systems.

Finally, Chapter 5 concludes the thesis by summarizing key findings, highlighting contributions to the field, and providing recommendations for future research in the area of approximating invariant manifolds of Hamiltonian systems.

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